Comparing Fr\'echet-Urysohn filters with two pre-orders
S. Garcia-Ferreira, J. E. Rivera-G\'omez

TL;DR
This paper investigates Fréchet-Urysohn filters on the natural numbers, distinguishing them using two pre-orders, and constructs large chains and antichains within these filters based on the Rudin-Keisler order.
Contribution
It introduces a new classification of Fréchet-Urysohn filters using two pre-orders and constructs large ordered and antichain structures among these filters.
Findings
Constructed an RK-chain of size continuum above any FU-filter.
Established the existence of an infinite RK-antichain of FU-filters.
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.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Advanced Topology and Set Theory
