MHB Problem of the Week #109 - June 30th, 2014

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The discussion centers on the problem of whether every locally compact Hausdorff space is paracompact. It has been established that this is not the case, with the Tychonoff plank serving as a notable counterexample. The original poster acknowledges their incomplete solution but plans to provide further details later. No responses have been posted to the problem thus far. The conversation highlights the complexities within topology, particularly regarding the properties of different types of spaces.
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Here's this week's problem!

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Problem: Determine whether or not every locally compact Hausdorff space is paracompact.

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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
 
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No one answered this week's problem.

I don't have a complete solution prepared due to various things, so I will do my best to fill in the details sometime soon.

[sp]It turns out that not every locally compact Hausdorff space is paracompact. An interesting counterexample is the Tychonoff plank, which I will elaborate on soon.[/sp]
 

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