Every join-semilattice with smallest element is isomorphic to the semilattice of compact open sets of some space.

Abstract: The assertion belongs to the representation theory of partially ordered sets, to Non-Hausdorff topology and to domain theory,  but is (co-)motivated by algebraic questions about the analysis of structures that can be seen as global sections of a sheaf (like a ring or like a generalized product). I will first explain my interest in the statement of the title and then construct the asserted space in a functorial way.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.