English

Comparing Fr\'echet-Urysohn filters with two pre-orders

General Topology 2016-02-22 v1

Abstract

A filter \F\F on \w\w is called Fr\'echet-Urysohn if the space with only one non-isolated point \w{\F}\w \cup \{\F\} is a Fr\'echet-Urysohn space, where the neighborhoods of the non-isolated point are determined by the elements of \F\F. 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 RKRK-chain of size \c^+ which is RKRK-above of avery FUFU-filter. Also, we show that there is an infinite RKRK-antichain of FUFU-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}
}
R2 v1 2026-06-22T12:53:54.778Z