About: Collectionwise normal space

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Collectionwise normal space Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatPropertiesOfTopologicalSpaces, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FCollectionwise_normal_space&invfp=IFP_OFF&sas=SAME_AS_OFF

In mathematics, a topological space is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. A family of subsets of is called discrete when every point of has a neighbourhood that intersects at most one of the sets from .An equivalent definition of collectionwise normal demands that the above Ui (i ∈ I) are themselves a discrete family, which is stronger than pairwise disjoint. Some authors assume that is also a T1 space as part of the definition.

Attributes	Values
rdf:type	yago:WikicatSeparationAxioms yago:Abstraction100002137 yago:AuditoryCommunication107109019 yago:Communication100033020 yago:Maxim107152948 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:Saying107151380 yago:Speech107109196 yago:WikicatPropertiesOfTopologicalSpaces
rdfs:label	Collectionwise normal space (en) Espace collectivement normal (fr)
rdfs:comment	In mathematics, a topological space is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. A family of subsets of is called discrete when every point of has a neighbourhood that intersects at most one of the sets from .An equivalent definition of collectionwise normal demands that the above Ui (i ∈ I) are themselves a discrete family, which is stronger than pairwise disjoint. Some authors assume that is also a T1 space as part of the definition. (en) En mathématiques, un espace topologique X est dit collectivement normal s'il vérifie la propriété de séparation suivante, strictement plus forte que la normalité et plus faible que la paracompacité : X est séparé et pour toute famille discrète (Fi)i∈I de fermés de X, il existe une famille (Ui)i∈I d'ouverts disjoints telle que pour tout i, Fi ⊂ Ui. Tout sous-espace Fσ — en particulier tout fermé — d'un espace collectivement normal est collectivement normal. (fr)
dcterms:subject	Properties of topological spaces Separation axioms
Wikipage page ID	9715483 (xsd:integer)
Wikipage revision ID	1058878852 (xsd:integer)
Link from a Wikipage to another Wikipage	Moore space (topology) Metrizable space Monotonically normal space Compact space Neighbourhood (mathematics) Normal space Order topology Closure (topology) Cofinite topology Properties of topological spaces Pairwise disjoint Hausdorff space F-sigma Paracompact space Ryszard Engelking Countably compact space Separation axioms Hereditarily normal space Metrizable Metrization theorem Separated sets Subspace topology Topological space Collectionwise Hausdorff Closed subset T₁ space
sameAs	Collectionwise normal space Collectionwise normal space Collectionwise normal space Collectionwise normal space Collectionwise normal space
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Reflist dbt:Short_description dbt:Visible_anchor
has abstract	In mathematics, a topological space is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. A family of subsets of is called discrete when every point of has a neighbourhood that intersects at most one of the sets from .An equivalent definition of collectionwise normal demands that the above Ui (i ∈ I) are themselves a discrete family, which is stronger than pairwise disjoint. Some authors assume that is also a T1 space as part of the definition. The property is intermediate in strength between paracompactness and normality, and occurs in metrization theorems. (en) En mathématiques, un espace topologique X est dit collectivement normal s'il vérifie la propriété de séparation suivante, strictement plus forte que la normalité et plus faible que la paracompacité : X est séparé et pour toute famille discrète (Fi)i∈I de fermés de X, il existe une famille (Ui)i∈I d'ouverts disjoints telle que pour tout i, Fi ⊂ Ui. Tout sous-espace Fσ — en particulier tout fermé — d'un espace collectivement normal est collectivement normal. Tout espace monotonement normal — en particulier tout espace métrisable — est (héréditairement) collectivement normal. Un espace collectivement normal n'est pas nécessairement dénombrablement paracompact. Cependant, un théorème de Robert Lee Moore établit que tout espace de Moore collectivement normal est métrisable. (fr)
prov:wasDerivedFrom	wikipedia-en:Collectionwise_normal_space?oldid=1058878852&ns=0
page length (characters) of wiki page	4656 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Collectionwise_normal_space
is Link from a Wikipage to another Wikipage of	Moore metrization theorem Hereditarily collectionwise normal Collectionwise normal
is Wikipage redirect of	Moore metrization theorem Hereditarily collectionwise normal Collectionwise normal
is foaf:primaryTopic of	wikipedia-en:Collectionwise_normal_space

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 53 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software