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| Authors: | S Garcia-Ferreira V I Malykhin |
| Institution: | Instituto de Matematicas, Unidad Morelia (UNAM), Nicolás Romero 150, Morelia, Michoacan 58000, México ; State Academy of Management, Rjazanskij Prospekt 99, Moscow, Russia 109 542 |
| 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. |
| Keywords: | Ultrafilter MAD family Franklin compact space Rudin-Keisler order $p$-sequential $p$-Fr\'echet Urysohn ultra-sequential ultra-Fr\'echet-Urysohn |
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