Tree duplicates, $G_\delta$-diagonals and Gruenhage spaces
Functional Analysis
2022-06-14 v1 General Topology
Abstract
We present an example in ZFC of a locally compact, scattered Hausdorff non-Gruenhage space having a -diagonal. This answers a question posed by Orihuela, Troyanski and the author in a study of strictly convex norms on Banach spaces. In addition, we show that the Banach space of continuous functions admits a -smooth bump function.
Keywords
Cite
@article{arxiv.1102.0982,
title = {Tree duplicates, $G_\delta$-diagonals and Gruenhage spaces},
author = {Richard J. Smith},
journal= {arXiv preprint arXiv:1102.0982},
year = {2022}
}