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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
? Show that Y is path connected and simply connected.

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Solution Preview

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 ...

Solution Summary

Trivial Topology, Continuity and Connectedness are investigated.