Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cardinalities of topologies with small base   Let T be the family of open subsets of a topological space (not necessarily
Hausdorff or even T_0). We prove that if T has a base of cardinality <= mu,
lambda <= mu < 2^lambda, lambda strong limit of cofinality aleph_0, then T has
cardinality <= mu or >= 2^lambda. This is our main conclusion. First we prove
it under some set theoretic assumption, which is clear when lambda = mu ; then
we eliminate the assumption by a theorem on pcf from [Sh 460] motivated
originally by this. Next we prove that the simplest examples are the basic
ones; they occur in every example (for lambda = aleph_0 this fulfill a promise
from [Sh 454]). The main result for the case lambda = aleph_0 was proved in [Sh
454].

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess