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Inequilogical spaces, directed homology and noncommutative geometry. (English) Zbl 1079.18001

The author introduces a preordered version of equilogical spaces, called inequilogical spaces, as a possible setting for directed algebraic topology. This new structure is of much importance in noncommutative geometry.
The paper is extremely valuable for researchers in directed homology and noncommutative geometry. It covers a remarkable amount of output of this topic of research.

MSC:

18B30 Categories of topological spaces and continuous mappings (MSC2010)
54A05 Topological spaces and generalizations (closure spaces, etc.)
55P99 Homotopy theory
46L85 Noncommutative topology
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