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.)

  • $\begingroup$ I think, the additive group of nonstandard real numbers will be a counter example. $\endgroup$ – Moishe Kohan Oct 30 '13 at 21:03
  • $\begingroup$ That won't be connected, since it won't be Dedekind-complete. $\;$ $\endgroup$ – user57159 Oct 30 '13 at 21:05
  • $\begingroup$ Yes, I just realized this too. $\endgroup$ – Moishe Kohan Oct 30 '13 at 21:07
  • 1
    $\begingroup$ This question was asked and answered at MathOverflow: mathoverflow.net/questions/149754/… $\endgroup$ – user43208 Feb 21 '17 at 20:49

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