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Tag Archives: disjoint union topology
Topology: Continuous Maps
Continuity in Metric Spaces Following the case of real analysis, let’s define continuous functions via the usual ε-δ definition. Definition. Let (X, d) and (Y, d’) be two metric spaces. A function f : X → Y is said to be … Continue reading
Posted in Notes
Tagged advanced, continuity, disjoint union topology, homeomorphism, metric spaces, product topology, subspaces, topology
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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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