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.
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© 2001 Springer Science+Business Media New York
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Höhle, U. (2001). Categorical Basis of Topology. In: Many Valued Topology and its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1617-0_4
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DOI: https://doi.org/10.1007/978-1-4615-1617-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5643-1
Online ISBN: 978-1-4615-1617-0
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