Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inductive proof of the Feinstein-Heath Swiss cheese
  "classicalisation" theorem   A theory of allocation maps has been developed by J. F. Feinstein and M. J.
Heath in order to prove a theorem, using Zorn's lemma, concerning the compact
plane sets known as Swiss cheese sets. These sets are important since, as
domains, they provide a good source of examples in the theory of uniform
algebras and rational approximation. In this paper we take a more direct
approach when proving their theorem by using transfinite induction and
cardinality. An explicit reference to a theory of allocation maps is no longer
required. Instead we find that the repeated application of a single operation
developed from the final step of the proof by Feinstein and Heath is enough.

18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th