Categorical Basis of Topology

Ulrich Höhle
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Ulrich Höhle: Bergische Universität, Fachbereich Mathematik

Chapter Chapter 3 in Many Valued Topology and its Applications, 2001, pp 55-104 from Springer

Abstract: Abstract In this chapter we lay down the categorical formulation of the most important topological notions and axioms — e.g. Hausdorff’s separation axiom, regularity, compactness. Among other things we will present a categorical version of J. Dieudonné’s principle of continuous extension and give a categorical discussion of the Tychonov theorem. We start with the formulation of topological space objects based on a given category C.

Keywords: Topological Space; Closure Operator; Space Object; Universal Property; Categorical Basis (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-1617-0_4

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DOI: 10.1007/978-1-4615-1617-0_4

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