Publications - Jorge Picado

Research Papers
  1. Tensor products and relation quantales (with Marcel Erné)
         Algebra Universalis, to appear.

  2. Joins of closed sublocales (with Aleš Pultr and Anna Tozzi)
         Houston Journal of Mathematics, to appear.

  3. A Boolean extension of a frame and a representation of discontinuity (with Aleš Pultr)
         Quaestiones Mathematicae, to appear.

  4. Generating sublocales by subsets and relations: a tangle of adjunctions (with M. Andrew Moshier and Aleš Pultr)
         Algebra Universalis 78 (2017) 105-118.

  5. Perfectness in locales (with J. Gutiérrez García and Tomasz Kubiak)
         Quaestiones Mathematicae 40 (2017) 507-518.

  6. Localic maps constructed from open and closed parts (with Aleš Pultr)
         Categories and General Algebraic Structures with Applications 6 (2017) 21-35.
        (volume dedicated to the 90th birthday of Bernhard Banaschewski).

  7. New aspects of subfitness in frames and spaces (with Aleš Pultr)
         Applied Categorical Structures 24 (2016) 703-714.
         Review (ZB)

  8. A unified view of the Dedekind completion of point-free function rings (with J. Gutiérrez García and I. Mozo Carollo)
         Quaestiones Mathematicae 39 (2016) 991-1003.
         Review (MR)

  9. Normal semicontinuity and the Dedekind completion of pointfree function rings (with J. Gutiérrez García and I. Mozo Carollo)
         Algebra Universalis 75 (2016) 301-330.
         Review (ZB)

  10. On an aspect of scatteredness in the pointfree setting (with Richard N. Ball and Aleš Pultr)
         Portugaliae Mathematica 73 (2016) 139-152.
         Review (MR, ZB)

  11. Presenting the frame of the unit circle (with J. Gutiérrez García and I. Mozo Carollo)
         Journal of Pure and Applied Algebra 220 (2016) 976–1001.
         Review (ZB)

  12. On permutable pairs of quasi-uniformities (with Maria João Ferreira and Mack Matlabyana)
         Topology and its Applications 196 (2015) 260-273.
         Review (MR, ZB)

  13. More on subfitness and fitness (with Aleš Pultr)
         Applied Categorical Structures 23 (2015) 323-335.
         Review (MR, ZB)

  14. Notes on the product of locales (with Aleš Pultr)
         Mathematica Slovaca 65 (2015) 247-264.
         Review (MR, ZB)

  15. On the Dedekind completion of function rings (with I. Mozo Carollo and J. Gutiérrez García)
         Forum Mathematicum 27 (2015) 2551-2585.
         Review (MR, ZB)

  16. Notes on point-free real functions and sublocales (with J. Gutiérrez García and Aleš Pultr)
         Categorical Methods in Algebra and Topology, Textos de Matemática, DMUC, Vol. 46, 2014, pp. 167-200.

  17. Monotone normality and stratifiability from a pointfree point of view (with J. Gutiérrez García and M. A. de Prada Vicente)
         Topology and its Applications 168 (2014) 46-65.
         Review (MR, Zblatt)

  18. (Sub)Fit biframes and non-symmetric nearness (with Aleš Pultr)
         Topology and its Applications 168 (2014) 66-81.
         Review (MR, Zblatt)

  19. On the parallel between normality and extremal disconnectedness (with J. Gutiérrez García)
         Journal of Pure and Applied Algebra 218 (2014) 784-803.
         Review (MR, Zblatt)

  20. Notes on exact meets and joins (with Richard N. Ball and Aleš Pultr)
         Applied Categorical Structures 22 (2014) 699-714.
         Review (Zblatt)

  21. Insertion and extension results for pointfree complete regularity (with J. Gutiérrez García)
         Bulletin of the Belgian Mathematical Society - Simon Stevin 20 (2013) 675-687.
         Review (MR, Zblatt)

  22. Entourages, covers and localic groups (with Aleš Pultr)
         Applied Categorical Structures 21 (2013) 49-66.
         Review (MR, Zblatt)

  23. On strong inclusions and asymmetric proximities in frames (with Aleš Pultr)
         Order 29 (2012) 513-531.
         Review (MR, Zblatt)

  24. Extended real functions in pointfree topology (with B. Banaschewski and J. Gutiérrez García)
         Journal of Pure and Applied Algebra 216 (2012) 905-922.
         Review (MR, Zblatt)

  25. Rings of real functions in pointfree topology (with J. Gutiérrez García)
         Topology and its Applications 158 (2011) 2264-2278.
         Review (MR, Zblatt)

  26. The semicontinuous quasi-uniformity of a frame, revisited (with M. J. Ferreira)
         Quaestiones Mathematicae 34 (2011) 175-186.
         Review (MR)

  27. On the uniformization of lattice-valued frames (with J. Gutiérrez García, I. Mardones-Pérez and M.A. de Prada Vicente)
         Fuzzy Sets and Systems 166 (2011) 90-100.

  28. Cover quasi-uniformities in frames (with Aleš Pultr)
         Topology and its Applications 158 (2011) 869–881.
         Review (Zblatt)

  29. Insertion of continuous real functions on spaces, bispaces, ordered spaces and point-free spaces - a common root (with M. J. Ferreira and J. Gutiérrez García)
         Applied Categorical Structures 19 (2011) 469-487.
         Review (MR, Zblatt)

  30. How to deal with the ring of (continuous) real-valued functions in terms of scales (with Javier Gutiérrez García)
         Applied Topology: Recent progress for Computer Science, Fuzzy Mathematics and Economics (Proceedings of WiAT'10, Gandia, 2010),
         Editorial Universitat Politècnica de València, ISBN 978-84-8363-565-0, 2010, pgs. 19-30. Pdf file

  31. An invitation to localic real functions (with Javier Gutiérrez García and Tomasz Kubiak)
         Applied Topology: Recent progress for Computer Science, Fuzzy Mathematics and Economics (Proceedings of WiAT'10, Gandia, 2010),
         Editorial Universitat Politècnica de València, ISBN 978-84-8363-565-0, 2010, pgs. 119-129. Pdf file

  32. Localic real functions: a general setting (with Javier Gutiérrez García and Tomasz Kubiak)
         Journal of Pure and Applied Algebra 213 (2009) 1064-1074.
         Review (MR)

  33. Completely normal frames and real-valued functions (with M. J. Ferreira and J. Gutiérrez García)
         Topology and its Applications 156 (2009) 2932–2941.
         Review (Zblatt)

  34. Lower and upper regularizations of frame semicontinuous real functions (with J. Gutiérrez García and T. Kubiak)
         Algebra Universalis 60 (2009) 169-184.
         Review (Zblatt)

  35. Pointfree forms of Dowker's and Michael's insertion theorems (with J. Gutiérrez García and T. Kubiak)
         Journal of Pure and Applied Algebra 213 (2009) 98-108.
         Review (Zblatt)

  36. Uniform-type structures on lattice-valued spaces and frames (with J. Gutiérrez García, I. Mardones-Pérez and M.A. de Prada Vicente)
         Fuzzy Sets and Systems 159 (2008) 2469– 2487.
         Review (Zblatt)

  37. Monotone insertion and monotone extension of frame homomorphisms (with J. Gutiérrez García and T. Kubiak)
         Journal of Pure and Applied Algebra 212 (2008) 955-968.

  38. Ideals in Heyting semilattices and open homomorphisms (with Aleš Pultr and Anna Tozzi)
         Quaestiones Mathematicae 30 (2007) 391–405.
         Review (Zblatt)

  39. Point-finiteness in pointfree topology (with Maria João Ferreira)
         Applied Categorical Stuctures 15 (2007) 185–198.
         Review (MR)

  40. On the algebraic representation of semicontinuity (with J. Gutiérrez García)
         Journal of Pure and Applied Algebra 210 (2007) 299-306.

  41. Sublocale sets and sublocale lattices (with Aleš Pultr)
         Arch. Math. (Brno) 42 (2006) 409-418.
         Review (Zblatt)

  42. A new look at localic interpolation theorems
         Topology and its Applications 153 (2006) 3203-3218.
         Review (MR)

  43. The semicontinuous quasi-uniformity of a frame (with Maria João Ferreira)
          Kyungpook Mathematical Journal 46 (2006) 189-200.
         Review (Zblatt)

  44. Functorial quasi-uniformities on frames (with Maria João Ferreira)
         Applied Categorical Structures 13 (2005) 281-303.
         Review (MR)

  45. The Galois approach to uniform structures (with Maria João Ferreira)
         Quaestiones Mathematicae 28 (2005) 355-373.
         Review (MR)

  46. The quantale of Galois connections
         Algebra Universalis 52 (2004) 527 - 540.
         Review (MR)

  47. A method of constructing compatible quasi-uniformities for an arbitrary frame (with Maria João Ferreira)
         Kyungpook Mathematical Journal 44 (2004) No. 3, 415-442.
         Review (MR)

  48. The gauge of a uniform frame
         Applied Categorical Structures 10 (2002) 593-602.
         Review (Zblatt)

  49. Frames with transitive structures (with W. Hunsaker),
         Applied Categorical Structures 10 (2002) 63-79.
         Review (MR, Zblatt)

  50. On complete congruence lattices of join-infinite distributive lattices
         Algebra Universalis 44 (2000) 325-332.
         Review (Zblatt)

  51. A note on total boundedness (with W. Hunsaker),
         Acta Mathematica Hungarica 88 (2000) 25-34.

  52.  Structured frames by Weil entourages,
         Applied Categorical Structures 8 (2000) 351-366.
         Review (Zblatt)

  53.  Two theorems of Efremovic in pointfree context,
         Journal of Pure and Applied Algebra 141 (1999) 289-298.

  54.  Priestley duality within frames,
         Proceedings of the Workshop on Dualities, Interpretability and Ordered Structures (CAUL, September 1997), University of Lisbon, 1999, pp. 21-33. Abstract, Postscript file

  55.  Frame quasi-uniformities by entourages,
         Festschrift (on the occasion of the 60th birthday of Guillaume Brümmer) incorporating Proceedings Symposium on Categorical Topology (University of Cape Town 1994),
         Department of Mathematics, University of Cape Town, 1999, pp. 161-175. Abstract

  56.  Weil nearness spaces,
         Portugaliae Mathematica 55 (1998) 233-254.
         Review (Zblatt)

  57.  On extended frames,
         Comment. Math. Univ. Carolinae 36 (1995) 537-549. Abstract

  58.  Weil uniformities for frames,
         Comment. Math. Univ. Carolinae 36 (1995) 357-370.
         Review (MR, Zblatt)

  59.  Join-continuous frames, Priestley's duality and biframes,
         Applied Categorical Structures 2 (1994) 297-313.
         Review (MR)

  60.  On two extensions of Dickson's torsion theory,
         Communications in Algebra 21 (1993) 2749-2769.



Dissertations
  1.  Vizinhanças da Diagonal no Sentido de Weil em Reticulados Locais
         Dissertação de Doutoramento, Universidade de Coimbra, 1995 (166 pgs). Resumo

         English version: Weil Entourages in Pointfree Topology
         Ph. D. Thesis, University of Coimbra, 1995 (161 pgs). Abstract

  2.  Teorias de Torsão,
         Dissertação de Mestrado, Universidade de Coimbra, 1990 (100 pgs). Resumo

         English version: Torsion Theories
         M. Sc. Thesis, University of Coimbra, 1990 (99 pgs). Abstract


Books (authored)
  1.  Frames and locales: topology without points (with Aleš Pultr)
         Springer Basel, Series Frontiers in Mathematics, Vol. 28, xx + 400 pp., 2012 (ISBN: 978-3-0348-0153-9).
         Contents, Preface, ERRATA.
         Review (Zblatt, MR).

  2.  Locales treated mostly in a covariant way (with Aleš Pultr)
         Textos de Matemática, DMUC, Vol. 41, xi + 104 pp., 2008 (ISBN 978-972-8564-45-2).
         PDF file, ERRATA.
         Review (Zblatt, MR).

  3.  Olimpíadas de Matemática - Cat. B (with Paulo Oliveira)
         Volume 2, Texto Editores, Setembro de 2007, ISBN 978-972-47-3582-5.

  4.  Olimpíadas de Matemática - Cat. A (with Paulo Oliveira)
         Volume 2, Texto Editores, Setembro de 2007, ISBN 978-972-47-3581-8.

  5.  Olimpíadas de Matemática - Cat. B (with Paulo Oliveira)
         Volume 1, Texto Editores, Novembro de 2006, ISBN 978-972-47-3255-8.

  6.  Olimpíadas de Matemática - Cat. A (with Paulo Oliveira)
         Volume 1, Texto Editores, Novembro de 2006, ISBN 978-972-47-3254-1.



Books (chapters)
  1.  Das formas às fórmulas: estrutura e geometria das conchas marinhas
         in: Matemática do Planeta Terra
         IST Press, Lisboa, 2013, pp. 323-358.

  2.  Locales (with Aleš Pultr and Anna Tozzi)
         in: Categorical Foundations - Special Topics in Order, Topology, Algebra and Sheaf Theory
         Encyclopedia of Mathematics and its Applications, Vol. 97, Cambridge University Press, 2004, pp. 49-101.
         ERRATA, Review (Zblatt, MR, EMS).



Books (edited)
  1.  Categorical Methods in Algebra and Topology, a volume in honour of Manuela Sobral
         M. M. Clementino, G. Janelidze, J. Picado, L. Sousa, W. Tholen (Editors)
         Textos de Matemática, DMUC, Vol. 46, 292 pp., 2014.
         Table of Contents.

  2.  School on Category Theory and Applications
         M. M. Clementino, J. Picado, M. Sobral, L. Sousa (Editors)
         Textos de Matemática, DMUC, Vol. 21, iii + 159 pp., 1999.
         Contents, Review (MR).



Journals
  1.  Topology and its Applications 158(17), 2011 - Special volume dedicated to Eraldo Giuli
         (Maria Manuel Clementino, J. Picado, Walter Tholen, editors)
         Foreword.

  2.  CIM Bulletin
         (António Cateano, J. Picado, editors, 2004-2008).



Course Notes
  1. Álgebra Comutativa: textos de apoio,
          Notas de curso, Universidade de Coimbra, 2013.

  2. Anéis (revisitados): divisibilidade e factorização,
          Notas de curso, Universidade de Coimbra, 2011.

  3. Sobre semicontinuidade de funções reais: uma descrição algébrica,
          Lição Síntese, Universidade de Coimbra, 2008.
          English translation: On semicontinuity of real functions --- an algebraic description, 2008.

  4. Corpos e Equações Algébricas
          Relatório de unidade curricular, Universidade de Coimbra, 2008.

  5. Corpos e Equações Algébricas
          Notas de curso, Universidade de Coimbra, 2008
          (Primeira versão: Aulas de Álgebra II, 2005).

  6. Estruturas Discretas para a Engenharia Informática
          Notas de curso, Universidade de Coimbra, 2007 (Última versão: Agosto de 2014).

  7.   Apontamentos de Geometria Diferencial
          Notas de curso, Universidade de Coimbra (última versão: 2006).

  8.   Matemática Discreta,
          Relatório de disciplina, Universidade de Coimbra, 2003.

  9.   Tópicos de Teoria Combinatória
          Notas de curso, Universidade de Coimbra, 2002.

  10.   Matemática Finita
          Relatório de disciplina, Universidade de Coimbra, 2000.

  11.   Textos de apoio de Álgebra (com Manuela Sobral)
          Notas de curso, Universidade de Coimbra, 2000.

  12.   Topologia sem pontos
          Curso intensivo, Escola de Outono do CAUL, Lisboa, 1998.

  13.   Apontamentos de Álgebra
          Notas de curso, Universidade de Coimbra, 1998.

  14.   Tópicos de Matemática Finita
          Notas de curso, Universidade de Coimbra, 1997.

  15.   Matemática Discreta
          Minicurso, Actas do IX Encontro Regional da Sociedade Portuguesa de Matemática (Tomar, 1986) 153-194. Resumo



Other
  1. Truques e magia com códigos algébricos (com Estefani Moraes Moreira),
          Gazeta de Matemática 175 (2015) 20-29.

  2. Análise de um jogo solitário com a ajuda do corpo GF(4) (com Paula Mendes Martins),
          Boletim da Sociedade Portuguesa de Matemática 69 (2013) 51-58.

  3. Existe um Sudoku com 16 pistas? (com Paula Mendes Martins),
          Boletim da Sociedade Portuguesa de Matemática 66 (2012) 57-63.

  4. Prefácio a "Matemática & Comboios" de Helder Pinto,
          Sociedade Portuguesa de Matemática, Leituras em Matemática, vol. 7, 2010.

  5. Seashells: the plainness and beauty of their mathematical description,
          Loci (Vol. 1, March 2009), DOI: 10.4169/loci003294,
          Journal of the MAA Mathematical Sciences Digital Library.

  6. An interview with F. William Lawvere - Part Two (with Maria Manuel Clementino),
          CIM Bulletin 24 (2008) 21-28.

  7. An interview with F. William Lawvere - Part One (with Maria Manuel Clementino),
          CIM Bulletin 23 (2007) 23-27.

  8. An interview with Eduardo L. Ortiz,
          CIM Bulletin 22 (2007) 20-23.

  9. A descrição matemática das conchas e do seu crescimento (com Helder Pinto),
          Página do Atractor - Matemática Interactiva, www.atractor.pt/mat/conchas, 2007.

  10. A beleza matemática das conchas marinhas,
          Gazeta de Matemática 152 (2007) 10-15. PDF file

  11. Matemática sem palavras (com Helder Pinto),
          Página do Atractor - Matemática Interactiva, www.atractor.pt/mat/sem_palavras, 2006.

  12. An interview with Marcelo Viana (with Maria Manuel Clementino),
          CIM Bulletin 20 (2006) 25-30.

  13. A curvatura e a torção: como distinguir a forma de uma curva (com Helder Pinto),
          Página do Atractor - Matemática Interactiva, www.atractor.pt/mat/curvtor, 2006.

  14. A álgebra das tranças (com Domingos Lopes),
          Boletim da Sociedade Portuguesa de Matemática 54 (2006) 29-69. PDF file

  15. Conchas marinhas: a simplicidade e beleza da sua descrição matemática,
          www.mat.uc.pt/~picado/conchas (Abril 2006)

  16. Sistemas de Identificação com Algarismos de Controlo (com Helder Pinto),
          Página do Atractor - Matemática Interactiva, www.atractor.pt/mat/alg_controlo, 2006.

  17. An interview with Alexei Sossinsky,
          CIM Bulletin 19 (2005) 24-29.

  18.   Interview with Jean Pierre Bourguignon (with F. J. Craveiro de Carvalho),
          Intern. Math. Nachrichten 186 (2001) 25-34.

  19.   A álgebra dos sistemas de identificação: da aritmética modular aos grupos diedrais,
          Boletim da Sociedade Portuguesa de Matemática 44 (2001) 39-73. Resumo PDF file

  20.   A matemática dos Bilhetes de Identidade,
          Millenium 19 (2000) 279-299.

  21.   Vizinhanças da Diagonal no Sentido de Weil em Reticulados Locais: principais resultados, consequências e aplicações,
          Relatório, Universidade de Coimbra, 1997.

  22.   Mathematical competitions in Portugal,
          Mathematics Competitions 5 (1992) 86-91. Abstract

  23.   Olhar retrospectivo sobre as Olimpíadas Nacionais de Matemática 1991,
          Boletim da Sociedade Portuguesa de Matemática 21 (1991) 45-67.

  24.   Olimpíadas Internacionais de Matemática,
          Jornal de Mathematica Elementar 109 (1991) 8-12.

  25.   A Matemática e o real: um exemplo (a propósito de um problema olímpico),
          Jornal de Mathematica Elementar 108 (1991) 8-10.

  26.   XXX Olimpíadas Internacionais de Matemática, Relato da primeira participação portuguesa,
          Boletim da Sociedade Portuguesa de Matemática 14 (1989) 38-45.