About: Knaster's condition

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is named after Polish mathematician Bronisław Knaster. Furthermore, assuming MA, ccc implies Knaster's condition, making the two equivalent.

Property Value
dbo:abstract
  • In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is named after Polish mathematician Bronisław Knaster. Knaster's condition implies the countable chain condition (ccc), and it is sometimes used in conjunction with a weaker form of Martin's axiom, where the ccc requirement is replaced with Knaster's condition. Not unlike ccc, Knaster's condition is also sometimes used as a property of a topological space, in which case it means that the topology (as in, the family of all open sets) with inclusion satisfies the condition. Furthermore, assuming MA, ccc implies Knaster's condition, making the two equivalent. (en)
dbo:wikiPageID
  • 32926406 (xsd:integer)
dbo:wikiPageLength
  • 1287 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 861023360 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • In mathematics, a partially ordered set P is said to have Knaster's condition upwards (sometimes property (K)) if any uncountable subset A of P has an upwards-linked uncountable subset. An analogous definition applies to Knaster's condition downwards. The property is named after Polish mathematician Bronisław Knaster. Furthermore, assuming MA, ccc implies Knaster's condition, making the two equivalent. (en)
rdfs:label
  • Knaster's condition (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License