query: Show the continuous image of a compact set is compact.
positive_passages.docid: 28637
positive_passages.text: Proving continuous image of compact sets are compact
negative_passages.docid: 63529
negative_passages.text: How to show that this set is compact in $\ell^2$
negative_passages.docid: 64487
negative_passages.text: Continuous function and dense set
negative_passages.docid: 10531
negative_passages.text: Is the convex hull of a compact set compact?
negative_passages.docid: 26794
negative_passages.text: Metrizability of Hausdorff continuous image of compact metric space
negative_passages.docid: 47810
negative_passages.text: $C(X)$ is separable when $X$ is compact?
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
negative_passages.docid: 53859
negative_passages.text: Continuous image of separable space
negative_passages.docid: 66895
negative_passages.text: A condition for the image of a metrizable space to be metrizable
negative_passages.docid: 64260
negative_passages.text: Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
negative_passages.docid: 146146
negative_passages.text: Proof that a closed subset of a compact space is a compact space
negative_passages.docid: 74311
negative_passages.text: Proving that the Intersection of any Collection of Compact Sets is Compact
negative_passages.docid: 84512
negative_passages.text: The preimage of continuous function on a closed set is closed.
negative_passages.docid: 66334
negative_passages.text: How is every subset of the set of reals with the finite complement topology compact?
negative_passages.docid: 138167
negative_passages.text: Image of a normal space under a closed and continuous map is normal
negative_passages.docid: 122086
negative_passages.text: continuous function: preimage of closure of a set is closure of preimage
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact