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$p$-sequentiality and $p$-Fréchet-Urysohn property of Franklin compact spaces

Authors: S. Garcia-Ferreira and V. I. Malykhin
Journal: Proc. Amer. Math. Soc. 124 (1996), 2267-2273
MSC (1991): Primary 54A20, 54A35
MathSciNet review: 1327014
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Abstract: Franklin compact spaces defined by maximal almost disjoint families of subsets of $\omega $ are considered from the view of its $p$-sequentiality and $p$-Fréchet-Urysohn-property for ultrafilters $p\in \omega^*$. Our principal results are the following: CH implies that for every $P$-point $p\in \omega^*$ there are a Franklin compact $p$-Fréchet-Urysohn space and a Franklin compact space which is not $p$-Fréchet-Urysohn; and, assuming CH, for every Franklin compact space there is a $P$-point $q\in \omega^*$ such that it is not $q$-Fréchet-Urysohn. Some new problems are raised.

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Additional Information

S. Garcia-Ferreira
Affiliation: Instituto de Matematicas, Unidad Morelia (UNAM), Nicolás Romero 150, Morelia, Michoacan 58000, México

V. I. Malykhin
Affiliation: State Academy of Management, Rjazanskij Prospekt 99, Moscow, Russia 109 542

Keywords: Ultrafilter, MAD family, Franklin compact space, Rudin-Keisler order, $p$-sequential, $p$-Fr\'echet Urysohn, ultra-sequential, ultra-Fr\'echet-Urysohn
Received by editor(s): July 5, 1993
Received by editor(s) in revised form: January 27, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society