Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extraordinary dimension theories generated by complexes   We study the extraordinary dimension function dim_{L} introduced by
\v{S}\v{c}epin. An axiomatic characterization of this dimension function is
obtained. We also introduce inductive dimensions ind_{L} and Ind_{L} and prove
that for separable metrizable spaces all three coincide. Several results such
as characterization of dim_{L} in terms of partitions and in terms of mappings
into $n$-dimensional cubes are presented. We also prove the converse of the
Dranishnikov-Uspenskij theorem on dimension-raising maps.

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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nlin