query: If $X$ is not Hausdorff, then does $X$ have a compact subset that is not closed?
positive_passages.docid: 149220
positive_passages.text: If every compact set is closed, then is the space Hausdorff?
negative_passages.docid: 120135
negative_passages.text: Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
negative_passages.docid: 3708
negative_passages.text: How can I prove that compact subset iff sequentially compact in second countable topological spaces?
negative_passages.docid: 148994
negative_passages.text: $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
negative_passages.docid: 110744
negative_passages.text: How to prove that a compact set in a Hausdorff topological space is closed?
negative_passages.docid: 109374
negative_passages.text: Is the Discrete Topology on $X$ the Only One Containing All Infinite Subsets of $X$?
negative_passages.docid: 116663
negative_passages.text: If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
negative_passages.docid: 481
negative_passages.text: Can compact sets completey determine a topology?
negative_passages.docid: 64694
negative_passages.text: $C_{c}(X)$ is complete. then implies that $X$ is compact.
negative_passages.docid: 141642
negative_passages.text: Closure of a certain subset in a compact topological group
negative_passages.docid: 148403
negative_passages.text: Compact space and Hausdorff space
negative_passages.docid: 84492
negative_passages.text: Can $X$ have compact connected components?
negative_passages.docid: 99645
negative_passages.text: Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
negative_passages.docid: 20706
negative_passages.text: Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
negative_passages.docid: 11383
negative_passages.text: Disjoint compact sets in a Hausdorff space can be separated
negative_passages.docid: 154682
negative_passages.text: G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)