Abstract
This chapter provides an overview of small Dowker spaces. A normal space whose product with the closed unit interval I is not normal is called a Dowker space. The spaces are named for Hugh Dowker who proved a number of characterizations of the class of spaces for which X ×I is normal. One of his motivations for studying this class of spaces was the study of the so-called insertion property: X has the insertion property whenever f, g : X → ℝ such that f <g, g lower semicontinuous and f upper semicontinuous, there is a continuous h: X → ℝ such that f <h <g. Dowker proved the following characterization: For a normal space, the following are equivalent (1) X is countably paracompact; (2) X ×Y is normal for all infinite, compact metric spaces Y ; (3) X ×Y is normal for some infinite compact metric space Y ; and (4) X has the insertion property. In the chapter are discussed a variety of problems related to Dowker spaces.
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