Word.ws English Dictionary

distinguished open set

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.

Noun

distinguished open set (plural distinguished open sets)

  1. 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.

Forms of distinguished open set

pluraldistinguished open sets

Questions about distinguished open set

What does distinguished open set mean?
Distinguished open set means 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.
What part of speech is distinguished open set?
Distinguished open set is a noun.
What is the plural of distinguished open set?
The plural of distinguished open set is distinguished open sets.

Words near distinguished open set in the dictionary

  1. distinguishable
  2. distinguishableness
  3. distinguishably
  4. distinguished
  5. Distinguished Competition
  6. distinguished open set
  7. distinguished open sets
  8. distinguished professor
  9. distinguished professors
  10. distinguishedly
  11. distinguishedness

Source and license

Adapted from Wiktionary: distinguished open set (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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