(a,b) not homeomorphic to [a,b]

  • Thread starter JG89
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  • #1
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Homework Statement


Show that (0,1) is no homeomorphic to [0,1]


Homework Equations





The Attempt at a Solution



I understand the usual procedure for proving this - remove a point from each of the spaces and check for connectedness. My only question is, the topology on each space isn't specified. Do I assume it's the subspace topology or what?

In general, when given questions like this, with no topology given, do I just infer from the context of the question which topology I should use?
 

Answers and Replies

  • #2
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Nevermind guys. Looks like I need to pay more attention. My book says to assume the standard topology unless otherwise noted.
 
  • #3
Office_Shredder
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I understand the usual procedure for proving this - remove a point from each of the spaces and check for connectedness.

This is a pretty awesome way of proving they're not homeomorphic to be honest. I think most people would just show that one is compact and the other is not
 

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