Can someone help me to prove that continuity of function of two or more variables does not depends on the choice of norm? Thank you!
2026-04-07 14:35:18.1775572518
Relation between continuity of function and norm
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On $\mathbb R^n$, any two norms are equivalent and therefore any two norms induce the same topology. So, if a function from $\mathbb R^n$ into any topological space is continuous with respect to one of them, then it will also be continuous with respect to the other one.