Type: Article

Comparing Fréchet–Urysohn filters with two pre-orders

García-Ferreira, S.; Rivera-Gómez, J. E.;

Abstract:

A filter F on omega is called Frechet-Urysohn if the space with only one non-isolated point omega boolean OR {F} is a Frechet-Urysohn space, where the neighborhoods of the non-isolated point are determined by the elements of F. In this paper, we distinguish some Frechet-Urysohn filters by using two pre-orderings of filters: One is the Rudin- Keisler pre-order and the other one was introduced by Todorcevic-Uzcategui in [11]. We mainly construct an RK-chain of size c(+) which is RK-above of every FU-filter. Also, we show that there is an infinite RK-antichain of FU-filters