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

S. Garcia-Ferreira; J. E. Rivera-Gómez

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arXiv · 1602.06227

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

S. Garcia-Ferreira·J. E. Rivera-Gómez

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Abstract

A filter $\F$ on $\w$ is called Fr\'echet-Urysohn if the space with only one non-isolated point $\w \cup \{\F\}$ is a Fr\'echet-Urysohn space, where the neighborhoods of the non-isolated point are determined by the elements of $\F$. 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 $RK$-chain of size $\c^+$ which is $RK$-above of avery $FU$-filter. Also, we show that there is an infinite $RK$-antichain of $FU$-filters.

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BibTeX RIS

S. Garcia-Ferreira, J. E. Rivera-Gómez. 2016-02-19. Comparing Fr\'echet-Urysohn filters with two pre-orders. https://arxiv.org/abs/1602.06227

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