Comparing Fr\'echet-Urysohn filters with two pre-orders
General Topology
2016-02-22 v1
Abstract
A filter on is called Fr\'echet-Urysohn if the space with only one non-isolated point is a Fr\'echet-Urysohn space, where the neighborhoods of the non-isolated point are determined by the elements of . In this paper, we distinguish some Fr\'echet-Urysohn filters by using two pre-orderings of filters: One is the Rudin-Keisler pre-order and the other one was introduced by Todor\v{c}evi\'c-Uzc\'ategui in \cite{tu05}. In this paper, we construct an -chain of size \c^+ which is -above of avery -filter. Also, we show that there is an infinite -antichain of -filters.
Cite
@article{arxiv.1602.06227,
title = {Comparing Fr\'echet-Urysohn filters with two pre-orders},
author = {S. Garcia-Ferreira and J. E. Rivera-Gómez},
journal= {arXiv preprint arXiv:1602.06227},
year = {2016}
}