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Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Open_and_closed_maps> ?p ?o }

• Open_and_closed_maps abstract "In topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function which maps closed sets to closed sets. A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa.Open and closed maps are not necessarily continuous. Further, continuity is independent of openness and closedness in the general case and a continuous function may have one, both, or neither property; this fact remains true even if one restricts oneself to metric spaces. Although their definitions seem more natural, open and closed maps are much less important than continuous maps. Recall that, by definition, a function f : X → Y is continuous if the preimage of every open set of Y is open in X. (Equivalently, if the preimage of every closed set of Y is closed in X).Early study of open maps was pioneered by Simion Stoilow and Gordon Thomas Whyburn.".
• Open_and_closed_maps wikiPageID "372090".
• Open_and_closed_maps wikiPageLength "14091".
• Open_and_closed_maps wikiPageOutDegree "59".
• Open_and_closed_maps wikiPageRevisionID "677333909".
• Open_and_closed_maps wikiPageWikiLink Angle.
• Open_and_closed_maps wikiPageWikiLink Banach_space.
• Open_and_closed_maps wikiPageWikiLink Base_(topology).
• Open_and_closed_maps wikiPageWikiLink Bijection.
• Open_and_closed_maps wikiPageWikiLink Bijective.
• Open_and_closed_maps wikiPageWikiLink Category:Continuous_mappings.
• Open_and_closed_maps wikiPageWikiLink Category:General_topology.
• Open_and_closed_maps wikiPageWikiLink Category:Lemmas.
• Open_and_closed_maps wikiPageWikiLink Closed_set.
• Open_and_closed_maps wikiPageWikiLink Closure_(topology).
• Open_and_closed_maps wikiPageWikiLink Compact_space.
• Open_and_closed_maps wikiPageWikiLink Complex_analysis.
• Open_and_closed_maps wikiPageWikiLink Complex_plane.
• Open_and_closed_maps wikiPageWikiLink Connected_space.
• Open_and_closed_maps wikiPageWikiLink Continuous_function.
• Open_and_closed_maps wikiPageWikiLink Continuous_function_(topology).
• Open_and_closed_maps wikiPageWikiLink Covering_map.
• Open_and_closed_maps wikiPageWikiLink Covering_space.
• Open_and_closed_maps wikiPageWikiLink Discrete_space.
• Open_and_closed_maps wikiPageWikiLink Discrete_topology.
• Open_and_closed_maps wikiPageWikiLink Embedding.
• Open_and_closed_maps wikiPageWikiLink Fiber_bundle.
• Open_and_closed_maps wikiPageWikiLink Floor_and_ceiling_functions.
• Open_and_closed_maps wikiPageWikiLink Floor_function.
• Open_and_closed_maps wikiPageWikiLink Function_(mathematics).
• Open_and_closed_maps wikiPageWikiLink Function_composition.
• Open_and_closed_maps wikiPageWikiLink Functional_analysis.
• Open_and_closed_maps wikiPageWikiLink Gordon_Thomas_Whyburn.
• Open_and_closed_maps wikiPageWikiLink Hausdorff_space.
• Open_and_closed_maps wikiPageWikiLink Holomorphic_function.
• Open_and_closed_maps wikiPageWikiLink Homeomorphism.
• Open_and_closed_maps wikiPageWikiLink If_and_only_if.
• Open_and_closed_maps wikiPageWikiLink Image_(mathematics).
• Open_and_closed_maps wikiPageWikiLink Injection_(mathematics).
• Open_and_closed_maps wikiPageWikiLink Injective_function.
• Open_and_closed_maps wikiPageWikiLink Integer.
• Open_and_closed_maps wikiPageWikiLink Interval_(mathematics).
• Open_and_closed_maps wikiPageWikiLink Invariance_of_domain.
• Open_and_closed_maps wikiPageWikiLink Linear_map.
• Open_and_closed_maps wikiPageWikiLink Linear_operator.
• Open_and_closed_maps wikiPageWikiLink Locally_compact_space.
• Open_and_closed_maps wikiPageWikiLink Manifold.
• Open_and_closed_maps wikiPageWikiLink Necessary_condition.
• Open_and_closed_maps wikiPageWikiLink Necessity_and_sufficiency.
• Open_and_closed_maps wikiPageWikiLink Neighborhood_(topology).
• Open_and_closed_maps wikiPageWikiLink Neighbourhood_(mathematics).
• Open_and_closed_maps wikiPageWikiLink Open_mapping_theorem_(complex_analysis).
• Open_and_closed_maps wikiPageWikiLink Open_mapping_theorem_(functional_analysis).
• Open_and_closed_maps wikiPageWikiLink Open_set.
• Open_and_closed_maps wikiPageWikiLink Preimage.
• Open_and_closed_maps wikiPageWikiLink Product_(topology).
• Open_and_closed_maps wikiPageWikiLink Product_topology.
• Open_and_closed_maps wikiPageWikiLink Proper_map.
• Open_and_closed_maps wikiPageWikiLink Quasi-open_map.
• Open_and_closed_maps wikiPageWikiLink Quotient_map.
• Open_and_closed_maps wikiPageWikiLink Quotient_space_(topology).
• Open_and_closed_maps wikiPageWikiLink Real_number.
• Open_and_closed_maps wikiPageWikiLink Simion_Stoilow.
• Open_and_closed_maps wikiPageWikiLink Sufficient_condition.
• Open_and_closed_maps wikiPageWikiLink Surjection.
• Open_and_closed_maps wikiPageWikiLink Surjective_function.
• Open_and_closed_maps wikiPageWikiLink Topological_embedding.
• Open_and_closed_maps wikiPageWikiLink Topological_space.
• Open_and_closed_maps wikiPageWikiLink Topology.
• Open_and_closed_maps wikiPageWikiLink Tube_lemma.
• Open_and_closed_maps wikiPageWikiLink Unit_circle.
• Open_and_closed_maps wikiPageWikiLinkText "Closed map lemma".
• Open_and_closed_maps wikiPageWikiLinkText "Open and closed maps".
• Open_and_closed_maps wikiPageWikiLinkText "open and closed maps".
• Open_and_closed_maps hasPhotoCollection Open_and_closed_maps.
• Open_and_closed_maps wikiPageUsesTemplate Template:Reflist.
• Open_and_closed_maps subject Category:Continuous_mappings.
• Open_and_closed_maps subject Category:General_topology.
• Open_and_closed_maps subject Category:Lemmas.
• Open_and_closed_maps hypernym Function.
• Open_and_closed_maps type Article.
• Open_and_closed_maps type ProgrammingLanguage.
• Open_and_closed_maps type Article.
• Open_and_closed_maps type Function.
• Open_and_closed_maps type Lemma.
• Open_and_closed_maps type Mapping.
• Open_and_closed_maps type Theorem.
• Open_and_closed_maps comment "In topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function which maps closed sets to closed sets. A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa.Open and closed maps are not necessarily continuous.".
• Open_and_closed_maps label "Open and closed maps".
• Open_and_closed_maps sameAs Aplicacions_obertes_i_aplicacions_tancades.
• Open_and_closed_maps sameAs Funciones_abiertas_y_cerradas.
• Open_and_closed_maps sameAs Applications_ouvertes_et_fermées.
• Open_and_closed_maps sameAs Funzione_aperta.
• Open_and_closed_maps sameAs 開写像と閉写像.
• Open_and_closed_maps sameAs 열린_사상과_닫힌_사상.
• Open_and_closed_maps sameAs Open_en_gesloten_afbeelding.
• Open_and_closed_maps sameAs Odwzorowania_otwarte_i_domknięte.
• Open_and_closed_maps sameAs m.020l0h.
• Open_and_closed_maps sameAs Öppna_och_slutna_avbildningar.
• Open_and_closed_maps sameAs Ánh_xạ_đóng_và_mở.

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