a point metric space X.show {a}^c is open.
Last edited by oaza; Dec 11th 2008 at 10:40 PM.
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Originally Posted by oaza Can someone help me with that proof. Let x be any point in a metric space X.Prove that {x}^c(complement of x) is open. I have the same problem to solve and also I do not know how to approach that.
Originally Posted by oaza Can someone help me with that proof. Originally Posted by oaza Let x be any point in a metric space X.Prove that {x}^c(complement of x) is open. Come on you two guys, this is such a fundamental property of metrics. The distance between two points in a metric space is positive.
That is really it?!!
Originally Posted by Plato Come on you two guys, this is such a fundamental property of metrics. The distance between two points in a metric space is positive. I always think proofs are supposed to be so long...lol is it really that simple?
Originally Posted by megamet2000 is it really that simple? That shows that the complement is the union of open balls.
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