Suppose we have two metric spaces $(X, \rho_x)$ and $(Y, \rho_y)$ and a uniformly continuous function $f\colon X \to Y$. The problem is to prove that image $f(A)$ of every precompact $A \subset X$ (i.e. a subspace whose closure in some larger space is compact) is also a precomact.
2025-01-12 23:33:02.1736724782
Image of a precompact under the action of uniformly continuous function is a precompact
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