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

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1996-07, Vol.124 (7), p.2267-2273
Main Authors: Garcia-Ferreira, S., Malykhin, V. I.
Format: Article
Language:English
Subjects:
Mathematical theorems
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-96-03322-9