Minimal bases, ideal extensions, and basic dualities. (English) Zbl 1128.06001

Erné, Marcel

Topol. Proc. 29, No. 2, 445-489 (2005).

The author introduces the concept of B-spaces (i.e., topological spaces with a smallest base). He investigates the relation of this concept to the concepts of algebraic domains and algebraic posets, provides a universal B-reflection for base spaces (i.e., topological spaces with a prescribed base), a universal B-sobrification, and establishes several equivalences and dualities between certain categories of spaces and categories of ordered sets.

Reviewer: Horst Herrlich (Bremen)

MSC:

06B35	Continuous lattices and posets, applications
54B05	Subspaces in general topology
18B30	Categories of topological spaces and continuous mappings (MSC2010)
54F05	Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54B30	Categorical methods in general topology

Keywords:

B-space; algebraic poset; continuous poset; Scott topology; base; sober