Dowker spaces. (English) Zbl 0554.54005

Rudin, Mary Ellen

Handbook of set-theoretic topology, 761-780 (1984).

[For the entire collection see Zbl 0546.00022.]
A Dowker space is a normal space whose Cartesian product with the closed interval is not normal (equivalently, which is not countably paracompact). The paper is a survey of results on the (non)existence of Dowker spaces satisfying certain additional conditions. The last section contains the proof of the homotopy extension theorem and a brief discussion of some classes of spaces related to the class of Dowker spaces.

Reviewer: J.Chaber

MSC:

54D15	Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54A35	Consistency and independence results in general topology

Keywords:

normality; countable paracompactness; (non)existence of Dowker spaces; homotopy extension theorem

Citations:

Zbl 0546.00022