PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 80 | 2 | 175-189
Tytuł artykułu

On quasi-p-bounded subsets

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of quasi-p-boundedness for p ∈ $ω^*$ is introduced and investigated. We characterize quasi-p-pseudocompact subsets of β(ω) containing ω, and we show that the concepts of RK-compatible ultrafilter and P-point in $ω^*$ can be defined in terms of quasi-p-pseudocompactness. For p ∈ $ω^*$, we prove that a subset B of a space X is quasi-p-bounded in X if and only if B × $P_{RK}(p)$ is bounded in X × $P_{RK}(p)$, if and only if $cl_{β(X × P_{RK}(p))}(B× P_{RK}(p)) = cl_{βX} B × β(ω)$, where $P_{RK}(p)$ is the set of Rudin-Keisler predecessors of p.
Rocznik
Tom
80
Numer
2
Strony
175-189
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-02-06
poprawiono
1998-09-28
Twórcy
autor
  • Departament de Matemàtiques, Universitat Jaume I, Campus de Penyeta Roja s/n 12071, Castelló, Spain
  • Departamento de Matemáticas, Facultad de Ciencias, U.N.A.M., Ciudad Universitaria, México 04510, México
Bibliografia
  • [1] A. R. Bernstein, A new kind of compactness for topological spaces, Fund. Math. 66 (1970), 185-193.
  • [2] J. L. Blasco, Two problems on $k_r$-spaces, Acta Math. Hungar. 32 (1978), 27-30.
  • [3] A. Blass and S. Shelah, There may be simple $P_{ℵ_1}$-points and $P_{ℵ_2}$-points and the Rudin-Keisler ordering may be downward directed, Ann. Pure Appl. Logic 33 (1987), 213-243.
  • [4] R. Engelking, General Topology, Polish Sci. Publ., Warszawa, 1977.
  • [5] Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87-91.
  • [6] Z. Frolík, The topological product of two pseudocompact spaces, Czechoslovak Math. J. 85 (1960), 339-349.
  • [7] S. García-Ferreira, Some generalizations of pseudocompactness, in: Ann. New York Acad. Sci. 728, New York Acad. Sci., 1994, 22-31.
  • [8] S. García-Ferreira, V. I. Malykhin and A. Tamariz-Mascarúa , Solutions and problems on convergence structures to ultrafilters, Questions Answers Gen. Topology 13 (1995), 103-122 .
  • [9] S. García-Ferreira, M. Sanchis and S. Watson , Some remarks on the product of $C_α$-compact subsets, Czechoslovak Math. J., to appear.
  • [10] J. Ginsburg and V. Saks, Some applications of ultrafilters in topology, Pacific J. Math. 57 (1975), 403-418.
  • [11] S. Hernández, M. Sanchis and M. Tkačenko , Bounded sets in spaces and topological groups, Topology Appl., to appear.
  • [12] A. Kato, A note on pseudocompact $k_r$-spaces, Proc. Amer. Math. Soc. 61 (1977), 175-176.
  • [13] M. Katětov, Characters and types of point sets, Fund. Math. 50 (1961), 367-380.
  • [14] M. Katětov, Products of filters, Comment. Math. Univ. Carolin. 9 (1968), 173-189.
  • [15] N. N. Noble, Ascoli theorems and the exponential map, Trans. Amer. Math. Soc. 143 (1969), 393-411.
  • [16] N. N. Noble, Countably compact and pseudocompact products, Czechoslovak Math. J. 19 (1969), 390-397.
  • [17] M. E. Rudin, Partial orders on the types of βℕ, Trans. Amer. Math. Soc. 155 (1971), 353-362.
  • [18] M. Sanchis and A. Tamariz-Mascarúa, $p$-pseudocompactness and related topics in topological spaces, Topology Appl., to appear.
  • [19] M. G. Tkačenko, Compactness type properties in topological groups, Czechoslovak Math. J. 113 (1988), 324-341.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv80i2p175bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.