Recent content by pacificguy

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    Graduate Is There a Bijection Between Metric Spaces A and B?

    Hi, If A and B are two metric spaces and there exists two onto functions F and G such that F:A->B and G:B->A, is there a way to prove that there exists a bijection mapping A to B?
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    Graduate Prove a map of a space onto itself is bijective

    Oh I guess you're right. Ok if A and B are two metric spaces and there exists two onto functions F and G such that F:A->B and G:B->A, is there a way to prove that there exists a bijection mapping A to B? The reason I'm asking is because I'm trying to prove a comment from Rudin that says there is...
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    Graduate F maps A onto A=>f is one to one

    Hi, Say f:A->A where A is a metric space and f is onto. I think it should be true that this implies that f is also one to one. Is there a way to formally prove this? Thanks.
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    Graduate Prove a map of a space onto itself is bijective

    Hi, Say F:A->A where A is a metric space and F is onto. I think it should be true that this implies that F is also one to one. Is there a way to formally prove this? Thanks.