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Question: let f rm gt rm be a function that maps...

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Let f: R^m -> R^m be a function that maps compact sets to compact sets and connected sets to connected sets. Prove that f is continuous. (answer below) but I have a question about it

Why is that first sentence true? And what is a "preserving" function? Does the term "regular" space refer to the separation axiom? clASSMAte Conmected linard J orded

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