query: Infinite subset of compact space has an accumulation point
positive_passages.docid: 16826
positive_passages.text: prove that every infinite subset of compact set H has a limit point (Explanation)
negative_passages.docid: 118508
negative_passages.text: Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
negative_passages.docid: 58471
negative_passages.text: Accumulation points of uncountable sets
negative_passages.docid: 60424
negative_passages.text: Uncountable family of uncountable compact subsets of $\mathbb{R}$
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 19566
negative_passages.text: Continuous images of compact sets are compact
negative_passages.docid: 146756
negative_passages.text: Convergence at infinitely many points in a compact set and convergence in the whole region
negative_passages.docid: 107614
negative_passages.text: Partitioning an infinite set
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 94485
negative_passages.text: Limit point compactness implies compactness.
negative_passages.docid: 95234
negative_passages.text: Quasi-components in compact space
negative_passages.docid: 106957
negative_passages.text: Compact sets are closed?
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 24266
negative_passages.text: Accumulation points of the set $S=\{(\frac {1} {n}, \frac {1} {m}) \space m, n \in \mathbb N\}$
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: 100560
negative_passages.text: $X$ compact Hausdorff space, characterize the maximal ideals of $C(X)$
negative_passages.docid: 158498
negative_passages.text: $A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$