Given Banach spaces $X$ and $Y$.
For precompactness: $$\tau\in\mathcal{C}(X,Y):\quad\overline{A}\text{ compact}\implies\overline{\tau(A)}\text{ compact}$$
Is this true and why?
2026-04-12 11:33:06.1775993586
Contraction: Precompactness
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For Hausdorff spaces: $$\overline{\tau(A)}\subseteq\overline{\tau({\overline{A}})}=\overline{\tau}(\overline{A})$$
Concluding compactness.