Page 9 - Textos de Matemática Vol. 41
P. 9

Contents vii
10 Separation I. Regular, fit and subfit 63
10.1 Regular,fitandsubfitlocales.................... 63 10.2 Hereditaryproperties ........................ 64 10.3 Somecharacterizationsoffitness.................. 64 10.4 Somecharacterizationsofsubfitness ................ 65 10.5 Twopropertiesofsubfitlocales................... 66 10.6 Anothercharacterizationoffitness................. 67
11 Separation II. Hausdorff axioms 69
11.1 Thediagonal............................. 69 11.2 Isbell-Hausdorffaxiom........................ 69 11.3 Hereditaryproperties ........................ 71 11.4 Dowker-Strauss-Hausdorffaxiom.................. 71 11.5 RelationbetweenthetwoHausdorffaxioms. . . . . . . . . . . . 72 11.6 RegularityandHausdorffproperties................ 72
12 Entourages and (quasi-)uniformities 75
12.1 Entourages.............................. 75 12.2 Compositionofentourages ..................... 76 12.3 Therelations1E and2E ...................... 81 12.4 Uniformitiesandquasi-uniformities . . . . . . . . . . . . . . . . 83 12.5 Basesandsubbases ......................... 84 12.6 Completeregularity ......................... 84 12.7 The biframe induced by a quasi-uniform locale . . . . . . . . . . 86 12.8 Localicgroups ............................ 87 12.9 Localicsubgroups .......................... 88 12.10Uniformitiesonlocalicgroups ................... 89
Bibliography 93 Index 99 Index of Notation 103



























































































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