Categorical Basis of Topology
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.
KeywordsTopological Space Closure Operator Space Object Universal Property Categorical Basis
Unable to display preview. Download preview PDF.