English

Gruenhage spaces and their influence on Banach space renorming theory

Functional Analysis 2024-12-06 v1 General Topology

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 GδG_\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.

Keywords

Cite

@article{arxiv.2412.04401,
  title  = {Gruenhage spaces and their influence on Banach space renorming theory},
  author = {Richard J. Smith},
  journal= {arXiv preprint arXiv:2412.04401},
  year   = {2024}
}