Categorical Topology : Proceedings of the L’Aquila Conference (1994)

This volume contains carefully selected and refereed papers presented at the International Workshop on Categorical Topology , held at the University of L'Aquila, L'Aquila, Italy from August 31 to September 4, 1994. This collection represents a wide range of current developments in the field, and will be of interest to mathematicians whose work involves category theory. Front Matter....Pages i-vii Compactness and the Axiom of Choice....Pages 1-14 On Categorical Notions of Compact Objects....Pages 15-29 Reflective Relatives of Adjunctions....Pages 31-41 The Katětov Dimension of Proximity Spaces....Pages 43-55 Generalized Reflective cum Coreflective Classes in Top and Unif....Pages 57-68 On the Largest Coreflective Cartesian Closed Subconstruct of Prtop ....Pages 69-79 Topological Spaces and Quasi-Varieties....Pages 81-85 α-Sober Spaces via the Orthogonal Closure Operator....Pages 87-95 Some Aspects of Topological Descent....Pages 97-106 The Pullback Closure Operator and Generalisations of Perfectness....Pages 107-120 A Remark on Fixed Points of Functors in Topological Categories....Pages 121-126 Concrete Categories Are Concretely Equivalent iff Their Uniquely Transportable Modifications Are Strict Concretely Isomorphic....Pages 127-128 Connectedness, Disconnectedness and Closure Operators, A More General Approach....Pages 129-138 Dold Type Theorems in Cubical Homotopy Theory....Pages 139-154 A Topological Banach Space Model of Linear Logic....Pages 155-162 Parametrizing the Theory of Closure Operators....Pages 163-174 Tychonoff compactifications and R -completions of mappings and rings of continuous functions....Pages 175-201 Disconnectednesses: Two Examples....Pages 203-212 Objects with dense diagonals....Pages 213-220 Ascoli-Arzelà-Theory based on continuous convergence in an (almost) non-Hausdorff setting....Pages 221-240 A Subcategory of FIL....Pages 241-244 Epis in the Category of Pairwise- T 2 Spaces....Pages 245-248 Clone segments in Top and in Unif....Pages 249-268 Simultaneous problems of clone segments in Top and in Unif....Pages 269-278 Back Matter....Pages 279-280