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

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.

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
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