query: Cross product of compact spaces is compact
positive_passages.docid: 29303
positive_passages.text: Cartesian product of compact sets is compact
negative_passages.docid: 6210
negative_passages.text: Countable compact spaces as ordinals
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 66180
negative_passages.text: Homomorphism between compact Hausdorff spaces.
negative_passages.docid: 123828
negative_passages.text: finite and infinite product of discrete space
negative_passages.docid: 133152
negative_passages.text: (X,d) be a compact metric space. For every open cover, show there exists ε > 0 such that ∀𝑥 ∈ X, B(x,ε) is contained in some member of the cover.
negative_passages.docid: 39076
negative_passages.text: Contraction of compact sets
negative_passages.docid: 14219
negative_passages.text: Is the intersection of a closed set and a compact set always compact?
negative_passages.docid: 97914
negative_passages.text: Contractive mapping on compact space
negative_passages.docid: 19566
negative_passages.text: Continuous images of compact sets are compact
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?
negative_passages.docid: 102048
negative_passages.text: Closure of a compact set in Regular space $ X $
negative_passages.docid: 22464
negative_passages.text: Which of the following subsets of   $\mathbb{R}^2$ are compact
negative_passages.docid: 11558
negative_passages.text: How to show that the limit of compact operators in the operator norm topology is compact
negative_passages.docid: 95831
negative_passages.text: Compactness and sequential compactness in metric spaces
negative_passages.docid: 3708
negative_passages.text: How can I prove that compact subset iff sequentially compact in second countable topological spaces?