Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 53, No. 4, pp. 397-433 (1996)

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Topology in a Category: Compactness

Maria Manuel Clementino, Eraldo Giuli and Walter Tholen

Departamento de Matemática, Universidade de Coimbra
Apartado 3008, 3000 Coimbra - PORTUGAL
E-mail: clementino@gemini.ci.uc.pt Dip. di Matematica Pura ed Applicata, Università degli Studi di L'Aquila,
67100 L'Aquila - ITALY
E-mail: giuli@aquila.infn.it Department of Mathematics and Statistics, York University,
Toronto - CANADA M3J 1P3
E-mail: tholen@mathstat.yorku.ca

Abstract: In a category with a subobject structure and a closure operator, we provide a categorical theory of compactness and perfectness which yields a number of classical results of general topology as special cases, including the product theorems by Tychonoff and Frolík, the existence of Stone-Cech compactifications, both for spaces and maps, and the Henriksen-Isbell characterization of perfect maps of Tychonoff spaces. Applications to other categories yield, among other things, an alternative proof for the productivity of categorically compact groups.

Keywords: Closure operator; Hausdorff object; compact object; compact morphism; perfect morphism.

Classification (MSC2000): 18B30, 54B30, 54D30, 54A05

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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