Preprints



On regular and homological closure operators
(with Gonçalo Gutierres)
Preprint 09-49 of Dep. Mat.Univ. Coimbra: pdf file

Abstract:
Observing that weak heredity of regular closure operators in Top and of homological closure operators in homological categories identifies torsion theories, we study these closure operators in parallel, showing that regular closure operators play the same role in topology as homological closure operators do algebraically.
 

Publications



On the categorical me
aning of Hausdorff and Gromov distances, I  (with Andrei Akhvlediani and Walter Tholen)
Topology and its Applications, available on line, doi:10.1016/j.topol.2009.06.018/.

Lawvere completeness in topology (with Dirk Hofmann).
Applied Categorical Structures 17 (2009) 175-210.

Exponentiable functors between quantaloid-enriched categories (with Dirk Hofmann and Isar Stubbe)
Applied Categorical Structures 17 (2009) 91-101.

Relative injectivity as cocompleteness for a class of distributors (with Dirk Hofmann)
Theory and Applications of Categories 21 (2009), 210-230.
 
Protolocalisations of homological categories (with Francis Borceux, Marino Gran and Lurdes Sousa)
Journal of Pure and Applied Algebra 212 (2008) 1898–1927.

On some special classes of continuous maps (with Dirk Hofmann)
Chapter 39, Part 4, of  Open Problems in Topology 2, pages 367-376, edited by Elliott Pearl, Elsevier 2007.

Torsion theories and radicals  in normal categories (with D. Dikranjan and W. Tholen)
Journal of Algebra 305 (2006) 98-129.
 
Topological protomodular algebras (with F. Borceux)
Topology and its Applications 153 (2006) 3085-3100.

Exponentiation in V-categories (with D. Hofmann)
Topology and its Applications 153 (2006) 3113-3128.

Topological semi-abelian algebras  (with F. Borceux)
Advances in Mathematics 190 (2005) 425-453.

Local homeomorphisms via ultrafilter convergence  (with Dirk Hofmann and George Janelidze)
Proceedings of the American Mathematical Society 133 (2005), 917-922.

Effective descent morphisms in categories of lax algebras   (with Dirk Hofmann)
Applied Categorical Structures 12 (2004) 413-425. 

On extensions of lax monads  (with D. Hofmann)
Theory and Applications of Categories 13 (2004) 41-60.

One setting for all: metric, topology, uniformity, approach structure (with Dirk Hofmann and Walter Tholen)
Applied Categorical Structures 12 (2004) 127-154. Abstract   

A Functional Approach to General Topology (with Eraldo Giuli and Walter Tholen),
in: Categorical Foundations. Special Topics in Order, Topology, Algebra, and Sheaf Theory,    
Encyclopedia of Mathematics and its Applications 97, Cambridge University Press (2004), pp. 103-163.

Exponentiability in categories of lax algebras   (with Dirk Hofmann and Walter Tholen)
Theory and Applications of Categories 11 (2003) 337-352.

Metric, Topology and Multicategory - A Common Approach (with Walter Tholen)
Journal of Pure and Applied Algebra 179 (2003) 13-47.

Topological features of lax algebras (with Dirk Hofmann)
Applied Categorical Structures 11 (2003) 267-286.

Topological features of lax algebras (with Dirk Hofmann)
Applied Categorical Structures 11 (2003) 267-286.

The convergence approach to exponentiable maps (with Dirk Hofmann and Walter Tholen)
Portugaliæ Mathematica 60 (2003) 139-160.

On limit stability of special classes of continuous maps (with Dirk Hofmann)
Topology and its Applications 125 (2002) 471-488.

Triquotient maps via ultrafilter convergence (with Dirk Hofmann)
Proceedings of the American Mathematical Society 130 (2002) 3423-3431.

On finite triquotient maps
Journal of Pure and Applied Algebra 168 (2002) 387-389.

A note on local compactness (with W. Tholen)
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, Suppl. 2, XXXII (2001) 17-31.

On connectedness via closure operators
Applied Categorical Structures 9 (2001) 539-556.

What is a quotient map with respect to a closure operator? (with E. Giuli and W. Tholen)
Applied Categorical Structures 9 (2001) 139-151.

Separated and connected maps (with W. Tholen)
Applied Categorical Structures 6 (1998) 373-401.

A Characterization of the Vietoris Topology (with W. Tholen)
Topology Proceedings 22 (1997) 71-95.

Separation versus connectedness (with W. Tholen)
Topology and its Applications 75 (1997) 143-181.

Tychonoff's Theorem in a Category (with W. Tholen)
Proceedings of the American Mathematical Society 124 (1996) 3311-3314.

Topology in a Category: Compactness (with E. Giuli and W. Tholen)
Portugaliæ Mathematica 53 (1996) 397-433.

On categorical notions of compact object
Applied Categorical Structures 4 (1996) 15-29.

Constant morphisms and constant subcategories
Applied Categorical Structures 3 (1995) 119-137.

On connectedness and disconnectedness
in: Topology with Applications (Szekszard, Hungary, 1993)
Mathematical Studies 4 (Bolyai Society), pgs. 71-82.

Weakly hereditary regular closure operators
Topology and its Applications 49 (1993) 129-139.

Hausdorff separation in categories
Applied Categorical Structures 1 (1993) 285-295.

T0- and T1-reflections
Comment. Mathematicae Universitatis Carolinae 33 (1992) 493-504.