-sequentiality and -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

DOI:
https://doi.org/10.1090/S0002-9939-96-03322-9

MathSciNet review:
1327014

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Abstract: Franklin compact spaces defined by maximal almost disjoint families of subsets of are considered from the view of its -sequentiality and -Fréchet-Urysohn-property for ultrafilters . Our principal results are the following: CH implies that for every -point there are a Franklin compact -Fréchet-Urysohn space and a Franklin compact space which is not -Fréchet-Urysohn; and, assuming CH, for every Franklin compact space there is a -point such that it is not -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

Email:
garcia@servidor.unam.mx, sgarcia@zeus.ccu.umich.mx

**V. I. Malykhin**

Affiliation:
State Academy of Management, Rjazanskij Prospekt 99, Moscow, Russia 109 542

Email:
matem@acman.msk.su

DOI:
https://doi.org/10.1090/S0002-9939-96-03322-9

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