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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 εδ 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 settheoretic 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, subbases, topology
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