-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 | References | Similar Articles | Additional Information
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