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

  • MHB
  • Thread starter Chris L T521
  • Start date
In summary, two individuals discuss the impact of technology and social media on today's society. One person argues that it has brought about positive changes, such as connecting people and promoting diversity. However, the other person believes that it has also brought negative effects, such as increased isolation and addiction. They both agree that moderation and responsible use are key in navigating the digital world.
  • #1
Chris L T521
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MHB
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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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  • #2
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]
 

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

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