Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tree duplicates, $G_\delta$-diagonals and Gruenhage spaces   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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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio