Concept

Spectral space

Summary
In mathematics, a spectral space is a topological space that is homeomorphic to the spectrum of a commutative ring. It is sometimes also called a coherent space because of the connection to coherent topos. Definition Let X be a topological space and let K\circ(X) be the set of all compact open subsets of X. Then X is said to be spectral if it satisfies all of the following conditions: *X is compact and T0.
  • K\circ(X) is a basis of open subsets of X.
  • K\circ(X) is closed under finite intersections.
  • X is sober, i.e., every nonempty irreducible closed subset of X has a (necessarily unique) generic point.
Equivalent descriptions Let X be a topological space. Each of the following properties are equivalent to the property of X being spectral: #X is homeomorphic to a projective limit of finite T0-spaces. #X is homeomorphic to the spectrum of a bounded distributive lattice L. In this case, L is isomorphic (as a bounded lattic
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading