Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexities and Representations of F-Borel Spaces   We investigate the $\mathcal F$-Borel complexity of topological spaces in
their different compactifcations. We provide a simple proof of the fact that a
space can have arbitrarily many different complexities in different
compactifications. We also develop a theory of representations of $\mathcal
F$-Borel sets, and show how to apply this theory to prove that the complexity
of hereditarily Lindel\"of spaces is absolute (that is, it is the same in every
compactification). We use these representations to characterize the
complexities attainable by a specific class of topological spaces. This
provides an alternative proof of the first result, and implies the existence of
a space with non-absolute additive complexity. We discuss the method used by
Talagrand to construct the first example of a space with non-absolute
complexity, hopefully providing an explanation which is more accessible than
the original one. We also discuss the relation of complexity and local
complexity, and show how to construct amalgamation-like compactifications.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs