- Geometry and Topology
Trivial Topology, Continuity and Connectedness
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Let X and Y be topological spaces, where the only open sets of Y are the empty set and Y itself, i.e., Y has the trivial topology.
? Show that any map X --> Y is continuous
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? Show that Y is path connected and simply connected.
1) Show that any map f:X->Y is continuous.
Recall, a map f:X->Y is continuous if for all open sets U in Y, f^(-1)(U) is open.
Since Y has the trivial topology, we only ...
Trivial Topology, Continuity and Connectedness are investigated.