Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On winning strategies for Banach-Mazur games   We give topological and game theoretic definitions and theorems nec- essary
for defining a Banach-Mazur game, and apply these definitions to formalize the
game. We then state and prove two theorems which give necessary conditions for
existence of winning strategies for players in a Banach-Mazur game.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
19
The categories of this paper are: eess