Is there a $\hspace{.01 in}\big($T$_{\hspace{.01 in}0}$$\hspace{-0.02 in}\big)\hspace{.01 in}$ topological group that is connected
and locally connected but is not path-connected?
(This question does not have the local connectedness condition.)
Asked
Active
Viewed 291 times
2
-
I think, the additive group of nonstandard real numbers will be a counter example. – Moishe Kohan Oct 30 '13 at 21:03
-
That won't be connected, since it won't be Dedekind-complete. $;$ – Oct 30 '13 at 21:05
-
Yes, I just realized this too. – Moishe Kohan Oct 30 '13 at 21:07
-
2This question was asked and answered at MathOverflow: http://mathoverflow.net/questions/149754/topological-group-that-is-connected-and-locally-connected-but-not-path-connected/ – user43208 Feb 21 '17 at 20:49