A combinatorial characterization of second category subsets of X^\omega
Logic
2007-05-23 v4 Mathematical Physics
General Topology
math.MP
Abstract
Let a finite non-empty X is equipped with discrete topology. We prove that S \subseteq X^\omega is of second category if and only if for each f:\omega -> \bigcup_{n \in \omega} X^n there exists a sequence {a_n}_{n \in \omega} belonging to S such that for infinitely many i \in \omega the infinite sequence {a_{i+n}}_{n \in \omega} extends the finite sequence f(i).
Keywords
Cite
@article{arxiv.math/9912056,
title = {A combinatorial characterization of second category subsets of X^\omega},
author = {Apoloniusz Tyszka},
journal= {arXiv preprint arXiv:math/9912056},
year = {2007}
}
Comments
with a counterexample by T. Bartoszynski, to appear in J. Nat. Geom