Matches in DBpedia 2014 for { ?s ?p In mathematics, the Szpilrajn extension theorem, due to Edward Szpilrajn (1930) (later called Edward Marczewski), is one of many examples of the use of the axiom of choice (in the form of Zorn's lemma) to find a maximal set with certain properties.The theorem states that, given a binary relation R that is irreflexive and transitive it is always possible to find an extension of the relation (i.e. a relation T that strictly includes R) which is asymmetric, negatively transitive and connected.First of all, we need some definitions to be clear upon the terminology we will use speaking about relations with particular properties.. }
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- Szpilrajn_extension_theorem abstract "In mathematics, the Szpilrajn extension theorem, due to Edward Szpilrajn (1930) (later called Edward Marczewski), is one of many examples of the use of the axiom of choice (in the form of Zorn's lemma) to find a maximal set with certain properties.The theorem states that, given a binary relation R that is irreflexive and transitive it is always possible to find an extension of the relation (i.e. a relation T that strictly includes R) which is asymmetric, negatively transitive and connected.First of all, we need some definitions to be clear upon the terminology we will use speaking about relations with particular properties.".