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Abstrakty
We study MB-representations of algebras and ideals when they are relativized to a subset, and when one considers the operations of sum and intersection for families of algebras and ideals. We observe that the algebras [wzór], on R are MB-representable under GCH. We find a class of topological spaces in which the algebra of clopen sets is MB-representable.
Wydawca
Czasopismo
Rocznik
Tom
Strony
275--286
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Institute of Mathematics Łódź Technical University Al. Politechniki 11 90-924 Łódź, Poland and Faculty of Mathematics University of Łódź Banacha 22 90-238 Łódź, Poland
- Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland
autor
- Institute of Mathematics, Łódź Technical University, Al. Politechniki 11, 90-924 Łódź, Poland
Bibliografia
- [1] Balcerzak, M., Bartoszewicz, A., Ciesielski, К., On Marczewski-Burstin representations of certain algebras of sets, Real Anal. Exchange 26 (2000/2001), 581-592.
- [2] Balcerzak, M., Bartoszewicz, A., Rzepecka, J., Wroński, S., Marczewski fields and ideals, Real Anal. Exchange 26 (2000/2001), 703-715.
- [3] Balcerzak, M., Roslanowski, A., On Mycielski ideals, Proc. Amer. Math. Soc. 110 (1990), 243-250.
- [4] Baldwin, S., The Marczewski hull property and complete Boolean algebras, Real Anal. Exchange, (to appear).
- [5] Brown, J. B., Elalaoui-Talibi, H., Marczewski-Burstin-like characterizations of algebras, ideals, and measurable functions, Colloq. Math. 82 (1999), 277-286.
- [6] Burstin, C., Eigenschaften messbaren und nichtmessbaren Mengen, Wien Ber. 123 (1914), 1525-1551.
- [7] Ciesielski, K.,5et Theory for the Working Mathematician, London Math. Soc. Stud. Texts 39, Cambridge Univ. Press, Cambridge, 1997.
- [8] Comfort, W. W., Garcia-Ferreira, S., Resolvability: a selective survey and some new results, Topology Appl. 74 (1996), 149-167.
- [9] Engelking, R., General Topology, PWN, Warsaw 1977.
- [10] Hewitt, E., A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309-333.
- [11] Kechris, A. S., Classical Descriptive Set Theory, Springer, New York, 1994.
- [12] Koppelberg, S., Handbook of Boolean Algebras, Vol. 1, Elsevier, Amsterdam, 1989.
- [13] Koszmider, R, unpublished notes.
- [14] Kuratowski, K., Topology, Vol.l, Academic Press, New York, 1966.
- [15] Miller, A. W., Special subsets of the real line, in: “Handbook of Set Theoretic Topology”, K. Kunen and J. E. Vaughan, eds., Elsevier, Amsterdam, 1984.
- [16] Monk, J. D., Appendix on set theory, in: “Handbook of Boolean Algebras”, Vol. 3, Elsevier, Amsterdam, 1989, 1215-1233.
- [17] Morgan II, J. C., Point Set Theory, Marcel Dekker, New York, 1990.
- [18] Mycielski, J., Some new ideals of sets on the real line, Colloq. Math. 20 (1969), 71-76.
- [19] Pawlikowski, J., Parametrized Ellentuck theorem, Topology Appl. 37 (1990), 65-73.
- [20] Roslanowski, A., On game ideals, Colloq. Math. 59 (1990), 159-168.
- [21] Rosłanowski, A., Mycielski ideals generated by uncountable systems, Colloq. Math. 66 (1994), 187-200.
- [22] Szpilrajn (Marczewski), E., Sur une classe de fonctions de M. Sierpiński et la classe correspondante d ’ensembles, Fund. Math. 24 (1935), 17-34.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-LOD6-0014-0034