query: Is there a name for a topological space $X$ in which every proper closed subset is compact?
positive_passages.docid: 111360
positive_passages.text: Topological spaces in which every proper closed subset is compact
negative_passages.docid: 106957
negative_passages.text: Compact sets are closed?
negative_passages.docid: 11383
negative_passages.text: Disjoint compact sets in a Hausdorff space can be separated
negative_passages.docid: 145415
negative_passages.text: Examples of almost compact spaces.
negative_passages.docid: 77563
negative_passages.text: Homeomorphism between spaces equipped with cofinite topologies
negative_passages.docid: 100121
negative_passages.text: Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
negative_passages.docid: 127900
negative_passages.text: Interior of closure of open set in topological space
negative_passages.docid: 99645
negative_passages.text: Metrizable topological space $X$ with every admissible metric complete then $X$ is compact
negative_passages.docid: 153573
negative_passages.text: Counter Example for the union of any number of compact sets is compact in T2-spaces
negative_passages.docid: 86782
negative_passages.text: A $T_4$ space satisfying that 'every continuous map from it to a Hausdorff space is a closed map' is compact.
negative_passages.docid: 50026
negative_passages.text: Product of compact and closed in topological group is closed
negative_passages.docid: 144400
negative_passages.text: Are compact subsets of metric spaces closed and bounded?
negative_passages.docid: 158814
negative_passages.text: Two definitions of locally compact space
negative_passages.docid: 100476
negative_passages.text: Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
negative_passages.docid: 6210
negative_passages.text: Countable compact spaces as ordinals
negative_passages.docid: 114608
negative_passages.text: Proof concerning regular space: there exist a closed set contained in any open set containing $x$
negative_passages.docid: 113227
negative_passages.text: Measure spaces are proper subsets