I know the result that in $R^n$ any open connected set is path connected. But I guess in general the result is not true in an arbitrary topological space.
Can anyone give an example showing this?
Thanks for your time.
2026-03-29 13:22:58.1774790578
Example for a set that is open connected but not path connected in an arbitrary topological space
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Any space $X$ that is connected, but not path-connected is a trivial example: $X$ is open in itself..