Assertion: set's subset | /r/HasAspect | supremum
Facets:
value: in a partially ordered set
type: OTHER
Source sentences:
text: Cantor had shown that every linearly ordered set \(S\) without endpoints that is dense (i.e., between any two different elements of \(S\) there is another one), complete (i.e., every subset of \(S\) that is bounded above has a supremum), and with a countable dense subset is isomorphic to the real line.
text: If in a partially ordered set P every bounded subset has a supremum, this applies also, for any set X, in the function space containing all functions from X to P,