Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonstandard homology theory for uniform spaces   We introduce a new homology theory of uniform spaces, provisionally called
$\mu$-homology theory. Our homology theory is based on hyperfinite chains of
microsimplices. This idea is due to McCord. We prove that $\mu$-homology theory
satisfies the Eilenberg-Steenrod axioms. The characterization of
chain-connectedness in terms of $\mu$-homology is provided. We also introduce
the notion of S-homotopy, which is weaker than uniform homotopy. We prove that
$\mu$-homology theory satisfies the S-homotopy axiom, and that every uniform
space can be S-deformation retracted to a dense subset. It follows that for
every uniform space $X$ and any dense subset $A$ of $X$, $X$ and $A$ have the
same $\mu$-homology. We briefly discuss the difference and similarity between
$\mu$-homology and McCord homology.

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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: econ