Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Relatively_compact_subspace> ?p ?o }
Showing triples 1 to 58 of
58
with 100 triples per page.
- Relatively_compact_subspace abstract "In mathematics, a relatively compact subspace (or relatively compact subset, or precompact) Y of a topological space X is a subset whose closure is compact.Since closed subsets of a compact space are compact, every subset of a compact space is relatively compact. In the case of a metric topology, or more generally when sequences may be used to test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X. Some major theorems characterise relatively compact subsets, in particular in function spaces. An example is the Arzelà–Ascoli theorem. Other cases of interest relate to uniform integrability, and the concept of normal family in complex analysis. Mahler's compactness theorem in the geometry of numbers characterises relatively compact subsets in certain non-compact homogeneous spaces (specifically spaces of lattices).The definition of an almost periodic function F at a conceptual level has to do with the translates of F being a relatively compact set. This needs to be made precise in terms of the topology used, in a particular theory.As a counterexample take any neighbourhood of the particular point of an infinite particular point space. The neighbourhood itself may be compact but is not relatively compact because its closure is the whole non-compact space.".
- Relatively_compact_subspace wikiPageExternalLink v=onepage&q&f=false.
- Relatively_compact_subspace wikiPageID "596600".
- Relatively_compact_subspace wikiPageLength "2104".
- Relatively_compact_subspace wikiPageOutDegree "22".
- Relatively_compact_subspace wikiPageRevisionID "672348093".
- Relatively_compact_subspace wikiPageWikiLink Almost_periodic_function.
- Relatively_compact_subspace wikiPageWikiLink Arzelà–Ascoli_theorem.
- Relatively_compact_subspace wikiPageWikiLink Category:Compactness_(mathematics).
- Relatively_compact_subspace wikiPageWikiLink Category:Properties_of_topological_spaces.
- Relatively_compact_subspace wikiPageWikiLink Closure_(topology).
- Relatively_compact_subspace wikiPageWikiLink Compact_space.
- Relatively_compact_subspace wikiPageWikiLink Compactly_embedded.
- Relatively_compact_subspace wikiPageWikiLink Complex_analysis.
- Relatively_compact_subspace wikiPageWikiLink Function_space.
- Relatively_compact_subspace wikiPageWikiLink Geometry_of_numbers.
- Relatively_compact_subspace wikiPageWikiLink Homogeneous_space.
- Relatively_compact_subspace wikiPageWikiLink Lattice_(group).
- Relatively_compact_subspace wikiPageWikiLink Mahlers_compactness_theorem.
- Relatively_compact_subspace wikiPageWikiLink Mathematics.
- Relatively_compact_subspace wikiPageWikiLink Metric_space.
- Relatively_compact_subspace wikiPageWikiLink Metric_topology.
- Relatively_compact_subspace wikiPageWikiLink Neighbourhood_(mathematics).
- Relatively_compact_subspace wikiPageWikiLink Neighbourhood_(topology).
- Relatively_compact_subspace wikiPageWikiLink Normal_family.
- Relatively_compact_subspace wikiPageWikiLink Particular_point_topology.
- Relatively_compact_subspace wikiPageWikiLink Sequence.
- Relatively_compact_subspace wikiPageWikiLink Topological_closure.
- Relatively_compact_subspace wikiPageWikiLink Topological_space.
- Relatively_compact_subspace wikiPageWikiLink Totally_bounded_space.
- Relatively_compact_subspace wikiPageWikiLink Uniform_integrability.
- Relatively_compact_subspace wikiPageWikiLinkText "Relatively compact subspace".
- Relatively_compact_subspace wikiPageWikiLinkText "Relatively_compact_subspace".
- Relatively_compact_subspace wikiPageWikiLinkText "pre-compact".
- Relatively_compact_subspace wikiPageWikiLinkText "precompact set".
- Relatively_compact_subspace wikiPageWikiLinkText "precompact".
- Relatively_compact_subspace wikiPageWikiLinkText "relatively compact".
- Relatively_compact_subspace hasPhotoCollection Relatively_compact_subspace.
- Relatively_compact_subspace subject Category:Compactness_(mathematics).
- Relatively_compact_subspace subject Category:Properties_of_topological_spaces.
- Relatively_compact_subspace hypernym Subset.
- Relatively_compact_subspace type Software.
- Relatively_compact_subspace type Property.
- Relatively_compact_subspace type Space.
- Relatively_compact_subspace comment "In mathematics, a relatively compact subspace (or relatively compact subset, or precompact) Y of a topological space X is a subset whose closure is compact.Since closed subsets of a compact space are compact, every subset of a compact space is relatively compact. In the case of a metric topology, or more generally when sequences may be used to test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X.".
- Relatively_compact_subspace label "Relatively compact subspace".
- Relatively_compact_subspace sameAs Relativně_kompaktní_množina.
- Relatively_compact_subspace sameAs Relativ_kompakte_Teilmenge.
- Relatively_compact_subspace sameAs Sottospazio_relativamente_compatto.
- Relatively_compact_subspace sameAs 相対コンパクト部分空間.
- Relatively_compact_subspace sameAs 상대_콤팩트_부분공간.
- Relatively_compact_subspace sameAs Podprzestrzeń_warunkowo_zwarta.
- Relatively_compact_subspace sameAs m.02tt59.
- Relatively_compact_subspace sameAs Compact_tương_đối.
- Relatively_compact_subspace sameAs Q610232.
- Relatively_compact_subspace sameAs Q610232.
- Relatively_compact_subspace wasDerivedFrom Relatively_compact_subspace?oldid=672348093.
- Relatively_compact_subspace isPrimaryTopicOf Relatively_compact_subspace.