Categorical Basis of Topology

  • Ulrich Höhle


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.


Topological Space Closure Operator Space Object Universal Property Categorical Basis 
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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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