Is Path Connectedness Enough for Local Path Connectedness?

[jojo12345]

Is there a space that is path connected but NOT locally path connected? I suspect that there must be some example because the theorem on the classification of covering spaces only applies to spaces that are, amongst other things, path connected and locally path connected.

 

[andlook]

https://www.physicsforums.com/showthread.php?t=234786

 

[jojo12345]

Thanks a lot!