About: K-topology

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In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties. Relative to the set of all real numbers carrying the standard topology, the set K = {1/n | n is a positive integer} is not closed since it doesn't contain its (only) limit point 0. Relative to the K-topology however, the set K is automatically decreed to be closed by adding ‘more’ basis elements to the standard topology on R. Basically, the K-topology on R is strictly finer than the standard topology on R. It is mostly useful for counterexamples in basic topology.

Attributes	Values
rdf:type	yago:WikicatCounterexamplesInTopology yago:WikicatTopologicalSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:Cognition100023271 yago:Counterexample105826832 yago:Disproof105826469 yago:Evidence105823932 yago:Information105816287 yago:MathematicalSpace108001685 yago:PsychologicalFeature100023100 yago:Set107999699 yago:Space100028651
rdfs:label	K-topologie (fr) K-topology (en)
rdfs:comment	In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties. Relative to the set of all real numbers carrying the standard topology, the set K = {1/n \| n is a positive integer} is not closed since it doesn't contain its (only) limit point 0. Relative to the K-topology however, the set K is automatically decreed to be closed by adding ‘more’ basis elements to the standard topology on R. Basically, the K-topology on R is strictly finer than the standard topology on R. It is mostly useful for counterexamples in basic topology. (en) En mathématiques, la K-topologie, ou topologie de Smirnov de la suite supprimée, est une topologie particulière sur l'ensemble ℝ des réels, plus fine que la topologie usuelle et pour laquelle l'ensemble K des inverses des entiers naturels non nuls est fermé (alors que pour la topologie usuelle, 0, qui n'appartient pas à K, est un point d'accumulation de K). D'autres propriétés remarquables de cet espace en font un contre-exemple utile en topologie générale. (fr)
dcterms:subject	Topological spaces
Wikipage page ID	18360606 (xsd:integer)
Wikipage revision ID	1111507860 (xsd:integer)
Link from a Wikipage to another Wikipage	Prentice Hall Limit point compact Compact space Mathematics Lower limit topology Neighbourhood (mathematics) Connected space Closed set Topological spaces Topology Hausdorff space Locally connected space Base (topology) Quotient space (topology) Regular space Natural number Sequence List of topologies Natural topology Topological space Basis (topology) Standard topology
sameAs	K-topology K-topology K-topology K-topology K-topology
dbp:wikiPageUsesTemplate	dbt:Cite_book
has abstract	In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties. Relative to the set of all real numbers carrying the standard topology, the set K = {1/n \| n is a positive integer} is not closed since it doesn't contain its (only) limit point 0. Relative to the K-topology however, the set K is automatically decreed to be closed by adding ‘more’ basis elements to the standard topology on R. Basically, the K-topology on R is strictly finer than the standard topology on R. It is mostly useful for counterexamples in basic topology. (en) En mathématiques, la K-topologie, ou topologie de Smirnov de la suite supprimée, est une topologie particulière sur l'ensemble ℝ des réels, plus fine que la topologie usuelle et pour laquelle l'ensemble K des inverses des entiers naturels non nuls est fermé (alors que pour la topologie usuelle, 0, qui n'appartient pas à K, est un point d'accumulation de K). D'autres propriétés remarquables de cet espace en font un contre-exemple utile en topologie générale. (fr)
gold:hypernym	Topology
prov:wasDerivedFrom	wikipedia-en:K-topology?oldid=1111507860&ns=0
page length (characters) of wiki page	3646 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:K-topology
is Link from a Wikipage to another Wikipage of	Gδ space Counterexamples in Topology List of topologies K topology
is Wikipage redirect of	K topology
is foaf:primaryTopic of	wikipedia-en:K-topology

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