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Tag Archives: metrisable topology
Topology: Separation Axioms
Motivation The separation axioms attempt to answer the following. Question. Given a topological space X, how far is it from being metrisable? We had a hint earlier: all metric spaces are Hausdorff, i.e. distinct points can be separated by two … Continue reading
Posted in Notes
Tagged advanced, Hausdorff, metrisable topology, normal, regular, separation axioms, T1, T2, T3, T4, topology, urysohn's lemma, urysohn's metrisation theorem
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Topology: Product Spaces (II)
The Box Topology Following an earlier article on products of two topological spaces, we’ll now talk about a product of possibly infinitely many topological spaces. Suppose is a collection of topological spaces indexed by I, and we wish to define … Continue reading
Topology: Disjoint Unions
Disjoint Unions Let X and Y be topological spaces and be a set-theoretic disjoint union. We wish to define a topology on Z in a most natural way. Definition. The topology on is defined to be: It’s almost trivial to check that this … Continue reading
Posted in Notes
Tagged advanced, bases, connected spaces, disjoint union topology, metrisable topology, product topology, sub-bases, topology
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Mathematics and Such 