distinguished open set

noun

A particularly basic kind of set, generalizing the notion of the complement of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the complement of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring.

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Meanings

noundistinguished open set (plural distinguished open sets)

plural distinguished open sets

  1. algebraic geometryA particularly basic kind of set, generalizing the notion of the complement of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the complement of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring.
Cite this entry
APA

distinguished open set. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/distinguished%20open%20set

MLA

“distinguished open set.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/distinguished%20open%20set. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “distinguished open set,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/distinguished%20open%20set.

Source: distinguished open set on Wiktionary, CC BY-SA 4.0.