How can I prove that every subset of R^n is homeomorphic to a closed subset of R^(n+1)? Does this only works for real number only as R is metrizable? Thanks.
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Hello. I haven't thought about the problem too deeply or anything, but it seems that the map defined by would do the trick. Did you try it?
But the inverse of f may not be continuous unless we restrict the range of inverse of f to the set in R^(n+1).
Isn't that what we're doing? We want a homeomorphism of into some subset of . In this case, we implicitly chose the subset .
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