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Categorical Basis of Topology

  • Ulrich Höhle

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Ulrich Höhle
    • 1
  1. 1.Fachbereich MathematikBergische UniversitätWuppertalGermany

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