About: Nested interval topology

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In mathematics, more specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers x such that 0 < x < 1. The open interval (0,1) is the set of all real numbers between 0 and 1; but not including either 0 or 1. To give the set (0,1) a topology means to say which subsets of (0,1) are "open", and to do so in a way that the following axioms are met:

Attributes	Values
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rdfs:label	Nested interval topology (en)
rdfs:comment	In mathematics, more specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers x such that 0 < x < 1. The open interval (0,1) is the set of all real numbers between 0 and 1; but not including either 0 or 1. To give the set (0,1) a topology means to say which subsets of (0,1) are "open", and to do so in a way that the following axioms are met: (en)
dcterms:subject	General topology
Wikipage page ID	28325444 (xsd:integer)
Wikipage revision ID	720295869 (xsd:integer)
Link from a Wikipage to another Wikipage	Compact space Mathematics General topology Closure (topology) Alexandrov topology Connected space Lindelof space Empty set Interval (mathematics) General topology Axiom Natural number Open interval Real number Set (mathematics) Subset T1 space Intersection (mathematics) Hausdorff topology Singleton set Union (mathematics) Irreducible space
sameAs	Nested interval topology Nested interval topology Nested interval topology
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In mathematics, more specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers x such that 0 < x < 1. The open interval (0,1) is the set of all real numbers between 0 and 1; but not including either 0 or 1. To give the set (0,1) a topology means to say which subsets of (0,1) are "open", and to do so in a way that the following axioms are met: 1. * The union of open sets is an open set. 2. * The finite intersection of open sets is an open set. 3. * The set (0,1) and the empty set ∅ are open sets. (en)
gold:hypernym	Example
prov:wasDerivedFrom	wikipedia-en:Nested_interval_topology?oldid=720295869&ns=0
page length (characters) of wiki page	2182 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Nested_interval_topology
is Link from a Wikipage to another Wikipage of	Counterexamples in Topology Nested Interval Topology
is Wikipage redirect of	Nested Interval Topology
is foaf:primaryTopic of	wikipedia-en:Nested_interval_topology

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