Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Paracompact_space> ?p ?o }
- Paracompact_space abstract "In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it admits partitions of unity subordinate to any open cover. Sometimes paracompact spaces are defined so as to always be Hausdorff.Every closed subspace of a paracompact space is paracompact. While compact subsets of Hausdorff spaces are always closed, this is not true for paracompact subsets. A space such that every subspace of it is a paracompact space is called hereditarily paracompact. This is equivalent to requiring that every open subspace be paracompact.Tychonoff's theorem (which states that the product of any collection of compact topological spaces is compact) does not generalize to paracompact spaces in that the product of paracompact spaces need not be paracompact. However, the product of a paracompact space and a compact space is always paracompact.Every metric space is paracompact. A topological space is metrizable if and only if it is a paracompact and locally metrizable Hausdorff space.".
- Paracompact_space wikiPageExternalLink paracompactness.
- Paracompact_space wikiPageID "48631".
- Paracompact_space wikiPageLength "20687".
- Paracompact_space wikiPageOutDegree "99".
- Paracompact_space wikiPageRevisionID "660911615".
- Paracompact_space wikiPageWikiLink A-paracompact_space.
- Paracompact_space wikiPageWikiLink A._H._Stone.
- Paracompact_space wikiPageWikiLink Arthur_Harold_Stone.
- Paracompact_space wikiPageWikiLink Axiom_of_choice.
- Paracompact_space wikiPageWikiLink Axiom_of_dependent_choice.
- Paracompact_space wikiPageWikiLink Bagpipe_theorem.
- Paracompact_space wikiPageWikiLink CW_complex.
- Paracompact_space wikiPageWikiLink Category:Compactness_(mathematics).
- Paracompact_space wikiPageWikiLink Category:Properties_of_topological_spaces.
- Paracompact_space wikiPageWikiLink Category:Separation_axioms.
- Paracompact_space wikiPageWikiLink Closed_set.
- Paracompact_space wikiPageWikiLink Compact_space.
- Paracompact_space wikiPageWikiLink Continuous_function.
- Paracompact_space wikiPageWikiLink Continuous_function_(topology).
- Paracompact_space wikiPageWikiLink Countable.
- Paracompact_space wikiPageWikiLink Countable_set.
- Paracompact_space wikiPageWikiLink Counterexamples_in_Topology.
- Paracompact_space wikiPageWikiLink Cover_(set_theory).
- Paracompact_space wikiPageWikiLink Cover_(topology).
- Paracompact_space wikiPageWikiLink Differential_form.
- Paracompact_space wikiPageWikiLink Discrete_space.
- Paracompact_space wikiPageWikiLink Euclidean_space.
- Paracompact_space wikiPageWikiLink Existential_quantification.
- Paracompact_space wikiPageWikiLink F-sigma_set.
- Paracompact_space wikiPageWikiLink Finite_set.
- Paracompact_space wikiPageWikiLink Fσ_set.
- Paracompact_space wikiPageWikiLink Hausdorff_space.
- Paracompact_space wikiPageWikiLink Infinite_(cardinality).
- Paracompact_space wikiPageWikiLink Infinite_set.
- Paracompact_space wikiPageWikiLink J._Arthur_Seebach,_Jr..
- Paracompact_space wikiPageWikiLink Jean_Dieudonné.
- Paracompact_space wikiPageWikiLink Journal_de_Mathématiques_Pures_et_Appliquées.
- Paracompact_space wikiPageWikiLink Lindelof_space.
- Paracompact_space wikiPageWikiLink Lindelöf_space.
- Paracompact_space wikiPageWikiLink Locally_compact.
- Paracompact_space wikiPageWikiLink Locally_compact_space.
- Paracompact_space wikiPageWikiLink Locally_finite_collection.
- Paracompact_space wikiPageWikiLink Locally_metrizable_space.
- Paracompact_space wikiPageWikiLink Long_line_(topology).
- Paracompact_space wikiPageWikiLink Lower_limit_topology.
- Paracompact_space wikiPageWikiLink Lynn_Arthur_Steen.
- Paracompact_space wikiPageWikiLink Lynn_Steen.
- Paracompact_space wikiPageWikiLink Manifold.
- Paracompact_space wikiPageWikiLink Mary_Ellen_Rudin.
- Paracompact_space wikiPageWikiLink Mathematics.
- Paracompact_space wikiPageWikiLink Metacompact.
- Paracompact_space wikiPageWikiLink Metacompact_space.
- Paracompact_space wikiPageWikiLink Metric_space.
- Paracompact_space wikiPageWikiLink Metrizable_space.
- Paracompact_space wikiPageWikiLink Metrization_theorem.
- Paracompact_space wikiPageWikiLink Michael_selection_theorem.
- Paracompact_space wikiPageWikiLink Neighborhood_(topology).
- Paracompact_space wikiPageWikiLink Neighbourhood_(mathematics).
- Paracompact_space wikiPageWikiLink Normal_space.
- Paracompact_space wikiPageWikiLink Open_cover.
- Paracompact_space wikiPageWikiLink Open_set.
- Paracompact_space wikiPageWikiLink Orthocompact_space.
- Paracompact_space wikiPageWikiLink Paracompact_space.
- Paracompact_space wikiPageWikiLink Paranormal_space.
- Paracompact_space wikiPageWikiLink Particular_point_topology.
- Paracompact_space wikiPageWikiLink Partition_of_unity.
- Paracompact_space wikiPageWikiLink Product_(topology).
- Paracompact_space wikiPageWikiLink Product_topology.
- Paracompact_space wikiPageWikiLink Prüfer_manifold.
- Paracompact_space wikiPageWikiLink Regular_space.
- Paracompact_space wikiPageWikiLink Second-countable_space.
- Paracompact_space wikiPageWikiLink Separation_axiom.
- Paracompact_space wikiPageWikiLink Separation_axioms.
- Paracompact_space wikiPageWikiLink Set_(mathematics).
- Paracompact_space wikiPageWikiLink Sheaf_cohomology.
- Paracompact_space wikiPageWikiLink Shrinking_space.
- Paracompact_space wikiPageWikiLink Sorgenfrey_line.
- Paracompact_space wikiPageWikiLink Sorgenfrey_plane.
- Paracompact_space wikiPageWikiLink Springer_Science+Business_Media.
- Paracompact_space wikiPageWikiLink Springer_Verlag.
- Paracompact_space wikiPageWikiLink Star_refinement.
- Paracompact_space wikiPageWikiLink Subset.
- Paracompact_space wikiPageWikiLink Subspace_(topology).
- Paracompact_space wikiPageWikiLink Subspace_topology.
- Paracompact_space wikiPageWikiLink Support_(mathematics).
- Paracompact_space wikiPageWikiLink T1_space.
- Paracompact_space wikiPageWikiLink Topological_manifold.
- Paracompact_space wikiPageWikiLink Topological_space.
- Paracompact_space wikiPageWikiLink Tube_lemma.
- Paracompact_space wikiPageWikiLink Tychonoffs_theorem.
- Paracompact_space wikiPageWikiLink Uncountable_set.
- Paracompact_space wikiPageWikiLink Union_(set_theory).
- Paracompact_space wikiPageWikiLink Unit_interval.
- Paracompact_space wikiPageWikiLink Universal_quantification.
- Paracompact_space wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Paracompact_space wikiPageWikiLink Čech_cohomology.
- Paracompact_space wikiPageWikiLinkText "Paracompact space".
- Paracompact_space wikiPageWikiLinkText "Paracompact space#Variations".
- Paracompact_space wikiPageWikiLinkText "Paracompact".