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Thread: subspaces and subsets in compact spaces

  1. #1 subspaces and subsets in compact spaces 
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    Hello. I have a homework problem that would easily follow from a few theorems if subsets and subspaces are equivalent in compact spaces.

    Are the definitions of subsets and subspaces equivalent when they are in a compact space?


    Thank you for your time.


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  3. #2  
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    Subspaces have to be spaces. Subsets can be anything.


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  4. #3  
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    Quote Originally Posted by EV33 View Post
    Are the definitions of subsets and subspaces equivalent when they are in a compact space?
    Yes, but only when the subsets are closed. You should be aware, we do not do your homework problems for you, but here is a hint:

    The closed subsets in a compact space are themselves compact. Why?

    Is every compact (sub)set of necessity a topological space? Why?
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