$p$-sequentiality and $p$-Fréchet-Urysohn property of Franklin compact spaces
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- by S. Garcia-Ferreira and V. I. Malykhin PDF
- Proc. Amer. Math. Soc. 124 (1996), 2267-2273 Request permission
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.References
- A. I. Baškirov, The classification of quotient maps and sequential bicompacta, Dokl. Akad. Nauk SSSR 217 (1974), 745–748 (Russian). MR 0358700
- A. I. Baškirov, Maximal almost disjoint systems and Franklin bicompacta, Dokl. Akad. Nauk SSSR 241 (1978), no. 3, 509–512 (Russian). MR 504217
- B. Boldjiev and V. Malyhin, The sequentiality is equivalent to the ${\scr F}$-Fréchet-Urysohn property, Comment. Math. Univ. Carolin. 31 (1990), no. 1, 23–25. MR 1056166
- S. P. Franklin, Spaces in which sequences suffice. II, Fund. Math. 61 (1967), 51–56. MR 222832, DOI 10.4064/fm-61-1-51-56
- Salvador García-Ferreira, On $\textrm {FU}(p)$-spaces and $p$-sequential spaces, Comment. Math. Univ. Carolin. 32 (1991), no. 1, 161–171. MR 1118299
- Salvador García-Ferreira and Angel Tamariz-Mascarúa, On $p$-sequential $p$-compact spaces, Comment. Math. Univ. Carolin. 34 (1993), no. 2, 347–356. MR 1241743
- Miroslav Katětov, Products of filters, Comment. Math. Univ. Carolinae 9 (1968), 173–189. MR 250257
- Ljubiša Kočinac, A generalization of chain-net spaces, Publ. Inst. Math. (Beograd) (N.S.) 44(58) (1988), 109–114. MR 995414
- A. P. Kombarov, On a theorem of A. Stone, Dokl. Akad. Nauk SSSR 270 (1983), no. 1, 38–40 (Russian). MR 705191
- V. I. Malyhin, Sequential bicompacta: Čech-Stone extensions and $\pi$-points, Vestnik Moskov. Univ. Ser. I Mat. Meh. 30 (1975), no. 1, 23–29 (Russian, with English summary). MR 0375236
- V. I. Malyhin, Sequential and Fréchet-Uryson bicompacta, Vestnik Moskov. Univ. Ser. I Mat. Meh. 31 (1976), no. 5, 42–48 (Russian, with English summary). MR 0487955
- V. I. Malychin, The sequentiality and the Fréchet-Urysohn property with respect to ultrafilters, Acta Univ. Carolin. Math. Phys. 31 (1990), no. 2, 65–69. 18th Winter School on Abstract Analysis (Srní, 1990). MR 1101417
- Ch. Mills, An easier proof of the Shelah $P$-point independence theorem (to appear).
- Cahit Arf, Untersuchungen über reinverzweigte Erweiterungen diskret bewerteter perfekter Körper, J. Reine Angew. Math. 181 (1939), 1–44 (German). MR 18, DOI 10.1515/crll.1940.181.1
- A. Szymański, The existence of $P(\alpha )$-points of $N^*$ for $\aleph _{0}<\alpha <{\mathfrak {c}}$, Colloq. Math. 37 (1977), no. 2, 179–184. MR 487992
- Edward L. Wimmers, The Shelah $P$-point independence theorem, Israel J. Math. 43 (1982), no. 1, 28–48. MR 728877, DOI 10.1007/BF02761683
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
- Received by editor(s): July 5, 1993
- Received by editor(s) in revised form: January 27, 1995
- Communicated by: Franklin D. Tall
- © Copyright 1996 American Mathematical Society
- 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