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- Q2528262 subject Q7452041.
- Q2528262 abstract "In mathematics, an upper set (also called an upward closed set or just an upset) of a partially ordered set (X,≤) is a subset U with the property that, if x is in U and x≤y, then y is in U.The dual notion is lower set (alternatively, down set, decreasing set, initial segment, semi-ideal; the set is downward closed), which is a subset L with the property that, if x is in L and y≤x, then y is in L.The terms order ideal or ideal are sometimes used as synonyms for lower set. This choice of terminology fails to reflect the notion of an ideal of a lattice because a lower set of a lattice is not necessarily a sublattice.".
- Q2528262 thumbnail Upset.svg?width=300.
- Q2528262 wikiPageExternalLink separation.pdf.
- Q2528262 wikiPageWikiLink Q1475294.
- Q2528262 wikiPageWikiLink Q1513048.
- Q2528262 wikiPageWikiLink Q1656686.
- Q2528262 wikiPageWikiLink Q177646.
- Q2528262 wikiPageWikiLink Q185359.
- Q2528262 wikiPageWikiLink Q185837.
- Q2528262 wikiPageWikiLink Q191780.
- Q2528262 wikiPageWikiLink Q2362924.
- Q2528262 wikiPageWikiLink Q242767.
- Q2528262 wikiPageWikiLink Q2528476.
- Q2528262 wikiPageWikiLink Q2754968.
- Q2528262 wikiPageWikiLink Q395.
- Q2528262 wikiPageWikiLink Q431937.
- Q2528262 wikiPageWikiLink Q4720939.
- Q2528262 wikiPageWikiLink Q474715.
- Q2528262 wikiPageWikiLink Q5141045.
- Q2528262 wikiPageWikiLink Q554403.
- Q2528262 wikiPageWikiLink Q7452041.
- Q2528262 comment "In mathematics, an upper set (also called an upward closed set or just an upset) of a partially ordered set (X,≤) is a subset U with the property that, if x is in U and x≤y, then y is in U.The dual notion is lower set (alternatively, down set, decreasing set, initial segment, semi-ideal; the set is downward closed), which is a subset L with the property that, if x is in L and y≤x, then y is in L.The terms order ideal or ideal are sometimes used as synonyms for lower set.".
- Q2528262 label "Upper set".
- Q2528262 depiction Upset.svg.