Matches in DBpedia 2016-04 for { ?s ?p "In topology, a compactly generated space (or k-space) is a topological space whose topology is coherent with the family of all compact subspaces. Specifically, a topological space X is compactly generated if it satisfies the following condition:A subspace A is closed in X if and only if A ∩ K is closed in K for all compact subspaces K ⊆ X.Equivalently, one can replace closed with open in this definition. If X is coherent with any cover of compact subspaces in the above sense then it is, in fact, coherent with all compact subspaces.A compactly generated Hausdorff space is a compactly generated space which is also Hausdorff. Like many compactness conditions, compactly generated spaces are often assumed to be Hausdorff."@en }
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- Compactly_generated_space abstract "In topology, a compactly generated space (or k-space) is a topological space whose topology is coherent with the family of all compact subspaces. Specifically, a topological space X is compactly generated if it satisfies the following condition:A subspace A is closed in X if and only if A ∩ K is closed in K for all compact subspaces K ⊆ X.Equivalently, one can replace closed with open in this definition. If X is coherent with any cover of compact subspaces in the above sense then it is, in fact, coherent with all compact subspaces.A compactly generated Hausdorff space is a compactly generated space which is also Hausdorff. Like many compactness conditions, compactly generated spaces are often assumed to be Hausdorff.".
- Q1738274 abstract "In topology, a compactly generated space (or k-space) is a topological space whose topology is coherent with the family of all compact subspaces. Specifically, a topological space X is compactly generated if it satisfies the following condition:A subspace A is closed in X if and only if A ∩ K is closed in K for all compact subspaces K ⊆ X.Equivalently, one can replace closed with open in this definition. If X is coherent with any cover of compact subspaces in the above sense then it is, in fact, coherent with all compact subspaces.A compactly generated Hausdorff space is a compactly generated space which is also Hausdorff. Like many compactness conditions, compactly generated spaces are often assumed to be Hausdorff.".