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Compactly generated space

In topology, a topological space X {\displaystyle X} is called a compactly generated space or k-space if its topology is determined by compact spaces in a manner made precise below. There is in fact no commonly agreed upon definition for such spaces, as different authors use variations of the definition that are not exactly equivalent to each other. Also…

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Motivation

Examples

Properties

K-ification

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Compactly generated space

Nodes76
Edges75
Triples125
Avg. degree1.97
Density0.026316
Components1

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Compactly generated space

Top relations

related to References · 55
Compactly generated space → Algebraic Topology, Arthur Jr, Berlin, Booksurge, Brown, Categories, CGWH, Charles, Chicago, Chicago Press, Compactly, Concise Course, Counterexamples, Dover, Dover Publications, General Topology, Graduate Texts, Groupoids, Heldermann Verlag, Inc
related to Motivation · 17
Compactly generated space → By, Compactly, CW-complex, CW-complexes, Dugundji, Félix, General Topology, German, Halperin, Hurewicz, Kelley, Rational Homotopy Theory, The, They, This, Thomas, Topology
related to K-ification · 14
Compactly generated space → CGHaus, CGTop, Denote, Given, Hausdorff, If, It, Let, One, Otherwise, The, This, Top, We
related to Subspaces · 13
Compactly generated space → Another, Arens, Arens-Fort, CG-1, Examples, For, Fortissimo, Hausdorff, In, It, Its, Subspaces, The
related to Examples · 10
Compactly generated space → As, CG-1, CG-2, CG-3, Definitions, For Hausdorff, Hausdorff, In, Such, This
related to Continuity of functions · 5
Compactly generated space → CG-1, If, More, Since, The
related to Products · 5
Compactly generated space → Both, For, Hausdorff, However, The
related to General framework for the definitions · 4
Compactly generated space → Let, The, There, These
is a · 1
Compactly generated space → space that is coherent with the family of its compact subspaces
related to Further reading · 1
Compactly generated space → Compactly

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Important terminology

displaystyle space spaces topology hausdorff generated compactly compact definition definitions cg-2 every cg-1 family category continuous closed subspaces quotient maps

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Compactly generated spaceis aspace that is coherent with the family of its compact subspaces0.90text
Compactly generated spacerelated to Continuity of functionsThe0.60section
Compactly generated spacerelated to Continuity of functionsMore0.60section
Compactly generated spacerelated to Continuity of functionsSince0.60section
Compactly generated spacerelated to Continuity of functionsIf0.60section
Compactly generated spacerelated to Continuity of functionsCG-10.60section
Compactly generated spacerelated to ExamplesAs0.60section
Compactly generated spacerelated to ExamplesDefinitions0.60section
Compactly generated spacerelated to ExamplesIn0.60section
Compactly generated spacerelated to ExamplesCG-10.60section
Compactly generated spacerelated to ExamplesCG-20.60section
Compactly generated spacerelated to ExamplesCG-30.60section

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