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In mathematics, particularly topology, a Gδ space is a topological space in which closed sets are in a way ‘separated’ from their complements using only countably many open sets. A Gδ space may thus be regarded as a space satisfying a different kind of separation axiom. In fact normal Gδ spaces are referred to as perfectly normal spaces, and satisfy the strongest of separation axioms. Gδ spaces are also called perfect spaces. The term perfect is also used, incompatibly, to refer to a space with no isolated points; see Perfect set.

Attributes	Values
rdfs:label	Gδ space (en) Совершенное пространство (ru)
rdfs:comment	In mathematics, particularly topology, a Gδ space is a topological space in which closed sets are in a way ‘separated’ from their complements using only countably many open sets. A Gδ space may thus be regarded as a space satisfying a different kind of separation axiom. In fact normal Gδ spaces are referred to as perfectly normal spaces, and satisfy the strongest of separation axioms. Gδ spaces are also called perfect spaces. The term perfect is also used, incompatibly, to refer to a space with no isolated points; see Perfect set. (en) Совершенное топологическое пространство — пространство, в котором каждое замкнутое множество является Gδ-множеством, то есть представимо в виде счётного пересечения открытых множеств. Майкл в 1953 году доказал, что совершенные пространства выдерживают умножение на метрические :Теорема: Произведение совершенного пространства и метризуемого пространства есть совершенное пространство. (ru)
dcterms:subject	General topology Real analysis
Wikipage page ID	17993945 (xsd:integer)
Wikipage revision ID	1043955809 (xsd:integer)
Link from a Wikipage to another Wikipage	Metrizable space Topological sum Intersection Lexicographic order topology on the unit square Normal space Tychonoff space G-delta set Closed set Perfect set Perfectly normal space Topology K-topology F-sigma set Isolated point Regular space Counterexamples in Topology First countable General topology Real analysis Open set Separation axioms Separation axiom Singleton (mathematics) Sorgenfrey plane Topological space T1 space Urysohn's metrization theorem Pseudometrizable space Sorgenfrey line Second countable Niemytzki plane Hereditarily Lindelöf
Link from a Wikipage to an external page	https://www.jstor.org/stable/2317335
sameAs	Gδ space Gδ space Gδ space Gδ space
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_book dbt:Reflist
has abstract	In mathematics, particularly topology, a Gδ space is a topological space in which closed sets are in a way ‘separated’ from their complements using only countably many open sets. A Gδ space may thus be regarded as a space satisfying a different kind of separation axiom. In fact normal Gδ spaces are referred to as perfectly normal spaces, and satisfy the strongest of separation axioms. Gδ spaces are also called perfect spaces. The term perfect is also used, incompatibly, to refer to a space with no isolated points; see Perfect set. (en) Совершенное топологическое пространство — пространство, в котором каждое замкнутое множество является Gδ-множеством, то есть представимо в виде счётного пересечения открытых множеств. Майкл в 1953 году доказал, что совершенные пространства выдерживают умножение на метрические :Теорема: Произведение совершенного пространства и метризуемого пространства есть совершенное пространство. Известно, что сами нормальность и наследственная нормальность не сохраняются при умножении на метризуемое пространство, однако произведение совершенно нормального пространства и метризуемого пространства остаётся совершенно нормальным! (ru)
gold:hypernym	’
prov:wasDerivedFrom	wikipedia-en:Gδ_space?oldid=1043955809&ns=0
page length (characters) of wiki page	4542 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Gδ_space
is Link from a Wikipage to another Wikipage of	Tychonoff plank Gδ set G-delta space G delta space
is Wikipage redirect of	G-delta space G delta space
is foaf:primaryTopic of	wikipedia-en:Gδ_space

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