Tree duplicates, $G_δ$-diagonals and Gruenhage spaces

Details Tree duplicates, $G_δ$-diagonals and Gruenhage spaces Tree duplicates, $G_δ$-diagonals and Gruenhage spaces

2011-02-04

arxiv.org/abs/1102.0982v1

Mathematics

Functional Analysis

Scientific paper

We present an example in ZFC of a locally compact, scattered Hausdorff
non-Gruenhage space $D$ having a $\G_delta$-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 $C_0(D)$ admits a $C^\infty$-smooth bump function.

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