Let f: (X1,d1) -> (X2, d2) be a continous function. Let C, a subset of X2 be compact. Is f^-1(C) ("f inverse") compact in X2? Having trouble finding a counterexample...
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Originally Posted by math_help Let f: (X1,d1) -> (X2, d2) be a continous function. Let C, a subset of X2 be compact. Is f^-1(C) ("f inverse") compact in X2? Having trouble finding a counterexample... I'm assuming that you mean Consider the function with the usual metric The one point set is compact in the range. (It is closed and bounded) but this set is unbouned and not compact.
What do you mean by saying I assume you mean X1?
Originally Posted by math_help What do you mean by saying I assume you mean X1? Is f^-1(C) ("f inverse") compact in X2? not
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