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arXiv · 2412.04401

Gruenhage spaces and their influence on Banach space renorming theory

Richard J. Smith
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Abstract

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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Richard J. Smith. 2024-12-05. Gruenhage spaces and their influence on Banach space renorming theory. https://arxiv.org/abs/2412.04401

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