Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the metrizability of spaces with a sharp base   A base $\mathcal{B}$ for a space $X$ is said to be sharp if, whenever $x\in
X$ and $(B_n)_{n\in\omega}$ is a sequence of pairwise distinct elements of
$\mathcal{B}$ each containing $x$, the collection $\{\bigcap_{j\le
n}B_j:n\in\omega\}$ is a local base at $x$. We answer questions raised by
Alleche et al. and Arhangel$'$ski\u{\i} et al. by showing that a pseudocompact
Tychonoff space with a sharp base need not be metrizable and that the product
of a space with a sharp base and $[0,1]$ need not have a sharp base. We prove
various metrization theorems and provide a characterization along the lines of
Ponomarev's for point countable bases.

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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: physics