About: Open and closed maps

Property	Value
dbo:description	funkcje zachowujące własność otwarcia i domknięcia zbioru (pl) funkcje zachowujące własność otwarcia i domknięcia zbioru (pl)
dbo:wikiPageWikiLink	dbr:Interior_(topology) dbr:Angle dbr:Linear_operator dbr:Floor_function dbr:Function_composition dbr:Local_homeomorphism dbr:Product_topology dbr:Complex_plane dbr:Function_(mathematics) dbr:Integer dbr:Real_number dbr:Topology dbr:Closed_set dbr:Closure_(topology) dbr:Interval_(mathematics) dbr:Codomain dbr:Homeomorphism dbr:Unit_circle dbr:Boundary_(topology) dbr:If_and_only_if dbr:Necessary_condition dbr:Sufficient_condition dbr:Proper_map dbr:Euclidean_topology dbr:Topological_vector_space dbr:Fiber_bundle dbr:Mathematics dbr:Complex_analysis dbr:Almost_open_map dbr:Open_set dbr:Connected_space dbr:Simion_Stoilow dbr:Open_mapping_theorem_(complex_analysis) dbr:Product_order dbc:General_topology dbr:Discrete_topology dbr:Topological_space dbr:Functional_analysis dbr:Holomorphic_function dbr:Manifold dbr:Invariance_of_domain dbr:Tube_lemma dbc:Lemmas dbr:Subspace_topology dbr:Logical_equivalence dbr:Surjective_function dbr:Base_(topology) dbr:Fiber_(mathematics) dbr:Subnet_(mathematics) dbr:Saturated_set dbr:Continuous_function dbr:Continuous_function_(topology) dbr:Bijection dbr:Injective_function dbr:Directed_set dbr:Compact_space dbr:Image_(mathematics) dbr:Net_(mathematics) dbr:Preimage dbr:Hausdorff_space dbr:Banach_space dbr:Locally_compact_space dbr:Open_mapping_theorem_(functional_analysis) dbr:List_of_set_identities_and_relations dbr:Gordon_Thomas_Whyburn dbr:Regular_open_set dbr:Hereditarily_quotient_map dbc:Continuous_mappings dbr:Basis_(topology) dbr:Bijective dbr:Continuous_map dbr:Convergent_net dbr:Coordinate_chart dbr:Neighborhood_(topology) dbr:Neighbourhood_basis dbr:Regular_closed_set dbr:Covering_map dbr:Injective dbr:Quotient_map dbr:Product_(topology) dbr:Topological_embedding dbr:Topological_interior dbr:Neighborhood__(topology)
dbp:group	note (en)
dbp:mathStatement	Every continuous function from a compact space to a Hausdorff space is closed and proper . (en) If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and (en)
dbp:name	dbr:Invariance_of_domain Closed map lemma (en)
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Anchor dbt:Sfn dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Trèves_François_Topological_vector_spaces,_distributions_and_kernels dbt:Visible_anchor dbt:Em dbt:Math_theorem dbt:Annotated_link dbt:Short_description
dct:subject	dbc:Theory_of_continuous_functions dbc:General_topology dbc:Lemmas
gold:hypernym	dbr:Function
rdfs:label	Open and closed maps (en) Aplicacions obertes i aplicacions tancades (ca) Funciones abiertas y cerradas (es) 開写像と閉写像 (ja) Applications ouvertes et fermées (fr) 열린 함수와 닫힌 함수 (ko) Odwzorowania otwarte i domknięte (pl) Open en gesloten afbeelding (nl) Öppna och slutna avbildningar (sv) 開映射和閉映射 (zh)
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prov:wasDerivedFrom	wikipedia-en:Open_and_closed_maps?oldid=1189898258&ns=0
foaf:isPrimaryTopicOf	wikipedia-en:Open_and_closed_maps
is dbo:knownFor of	dbr:Simion_Stoilow
is dbo:wikiPageRedirects of	dbr:Open_map dbr:Closed_map dbr:Open_&_closed_maps dbr:Open_function dbr:Open_mapping dbr:Closed_function dbr:Closed_map_(topology) dbr:Closed_map_lemma dbr:Closed_mapping dbr:Relatively_open_map dbr:Point_of_openness
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is foaf:primaryTopic of	wikipedia-en:Open_and_closed_maps