In order theory, a nucleus is a function F on a meet-semilattice 𝔄 such that (for every p in 𝔄):

  1. 1.


  2. 2.


  3. 3.


Usually, the term nucleus is used in frames and locales theory (when the semilattice 𝔄 is a frame).

1 Some well known results about nuclei

PropositionPlanetmathPlanetmathPlanetmath If F is a nucleus on a frame 𝔄, then the poset Fix(F) of fixed pointsPlanetmathPlanetmath of F, with order inherited from 𝔄, is also a frame.

Title Nucleus
Canonical name Nucleus
Date of creation 2014-12-18 15:34:14
Last modified on 2014-12-18 15:34:14
Owner porton (9363)
Last modified by porton (9363)
Numerical id 1
Author porton (9363)
Entry type Definition
Classification msc 06B99