Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of strongly proper dyadic subbases   We consider a topological space with its subbase which induces a coding for
each point. Every second-countable Hausdorff space has a subbase that is the
union of countably many pairs of disjoint open subsets. A dyadic subbase is
such a subbase with a fixed enumeration. If a dyadic subbase is given, then we
obtain a domain representation of the given space. The properness and the
strong properness of dyadic subbases have been studied, and it is known that
every strongly proper dyadic subbase induces an admissible domain
representation regardless of its enumeration. We show that every locally
compact separable metric space has a strongly proper dyadic subbase.

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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ