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Community Bot
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Is there a ($\mathrm{T}_0$) topological group that is connected and locally connected but is not path-connected?

This is a cross-post from MSE, since my question theremy question there was posted over three weeks ago and hasn't gotten anything useful. An earlier question of mineearlier question of mine from MSE did not specify local connectedness.

Is there a ($\mathrm{T}_0$) topological group that is connected and locally connected but is not path-connected?

This is a cross-post from MSE, since my question there was posted over three weeks ago and hasn't gotten anything useful. An earlier question of mine from MSE did not specify local connectedness.

Is there a ($\mathrm{T}_0$) topological group that is connected and locally connected but is not path-connected?

This is a cross-post from MSE, since my question there was posted over three weeks ago and hasn't gotten anything useful. An earlier question of mine from MSE did not specify local connectedness.

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Ricardo Andrade
Ricardo Andrade
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Is there a $\hspace{.02 in}\big($(T$_{\hspace{.01 in}0}$$\mathrm{T}_0$$\hspace{-0.02 in}\big)\hspace{.01 in}$) topological group that is connected and locally connected but is not path-connected?

This is a cross-post from MSE, since my question there was posted over three weeks ago and hasn't gotten anything useful. $\:$ An earlier question of mine from MSE did not specify local connectedness.
 

Is there a $\hspace{.02 in}\big($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 is a cross-post from MSE, since my question there was posted over three weeks ago and hasn't gotten anything useful. $\:$ An earlier question of mine from MSE did not specify local connectedness.
 

Is there a ($\mathrm{T}_0$) topological group that is connected and locally connected but is not path-connected?

This is a cross-post from MSE, since my question there was posted over three weeks ago and hasn't gotten anything useful. An earlier question of mine from MSE did not specify local connectedness.

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user5810
user5810

topological group that is connected and locally connected but not path-connected

Is there a $\hspace{.02 in}\big($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 is a cross-post from MSE, since my question there was posted over three weeks ago and hasn't gotten anything useful. $\:$ An earlier question of mine from MSE did not specify local connectedness.