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arXiv · 1102.0982

Tree duplicates, $G_\delta$-diagonals and Gruenhage spaces

Richard J. Smith
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Abstract

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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Richard J. Smith. 2011-02-04. Tree duplicates, $G_\delta$-diagonals and Gruenhage spaces. https://doi.org/10.1090/s0002-9939-2012-11142-6

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