Given, two compact sets A and B, how do we show that their intersection A B is also compact?
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Originally Posted by harish21 Given, two compact sets A and B, how do we show that their intersection A B is also compact? In what kind of space?
Originally Posted by Drexel28 In what kind of space? A and B are compact subsets of R
Originally Posted by harish21 A and B are compact subsets of R Think closed subspace
Originally Posted by Drexel28 Think closed subspace A and B are closed and bounded because they are compact. So A B is also closed. How do we show boundedness?
Originally Posted by harish21 A and B are closed and bounded because they are compact. So A B is also closed. How do we show boundedness? The Heine-Borel theorem is kind of overkill here...but. Clearly if then , right?
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