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Symmetric spaces, g-developable spaces and g-metrizable spaces. (English) Zbl 0732.54023

There are many generalizations of metric and developable spaces in the literature which are generated by relaxing the triangle inequality requirement and the requirement that the covers be made up of open sets. Many of these arise naturally in the study of certain quotients of metric and developable spaces. The author considers many such properties, but the particular emphasis is on the g-metrizable and g-developable spaces. He shows that there is an example of a regular g-developable space which is not semi-stratifiable. The example he uses is Gruenhage’s nonperfect symmetrizable space. These properties are generally very badly behaved with respect to products. The author shows that strong conditions are needed on the factors to have any hope g-developable or g-metrizable product. Many other results are given.

MSC:

54E30 Moore spaces
54D55 Sequential spaces
54E25 Semimetric spaces
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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