Gruenhage spaces and their influence on Banach space renorming theory
Keywords:
Gruenhage space, renorming theory, strict convexity, Gul'ko compact, descriptive compactAbstract
In a paper from 1987, Gruenhage defined a class of topological spaces that now bear his name, and used it to solve a problem of Talagrand on the existence of dense $G_\delta$ metrizable subsets of Gul'ko compact spaces. Gruenhage's paper became highly influential among researchers in renorming theory, a branch of Banach space theory. In this paper we survey Gruenhage and related spaces, and their interactions with renorming theory.
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