Real Analysis Exchange

MB-Representations and Topological Algebras

Artur Bartoszewicz and Krzysztof Ciesielski

Full-text: Open access


For an algebra $\mathcal{A}$ and an ideal $\mathcal{I}$ of subsets of a set $X$ we consider pairs $(\mathcal{A, I})$ which have the common inner Marczewski-Burstin representation. The main goal of the paper is to investigate which inner Marczewski-Burstin representable algebras and pairs are topological.

Article information

Real Anal. Exchange, Volume 27, Number 2 (2001), 749-756.

First available in Project Euclid: 2 June 2008

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54E52: Baire category, Baire spaces 06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45] 03E35: Consistency and independence results

Generalized Marczewski's sets topology


Bartoszewicz, Artur; Ciesielski, Krzysztof. MB-Representations and Topological Algebras. Real Anal. Exchange 27 (2001), no. 2, 749--756.

Export citation


  • B. Aniszczyk, Remarks on $\sigma$-algebra of $(s)$-measurable sets, Bull. Polish Acad. Sci. Math., 35(9–10) (1987), 561–563.
  • M. Balcerzak, A. Bartoszewicz, K. Ciesielski, On Marczewski-Burstin representations of certain algebras, Real Anal. Exchange, 26(2) (2000–2001), 581–591.
  • M. Balcerzak, A. Bartoszewicz, J. Rzepecka, S. Wroński, Marczewski fields and ideals, Real Anal. Exchange, 26(2) (2000–2001), 703–715.
  • M. Balcerzak, J. Rzepecka, Marczewski sets in the Hashimoto topologies for measure and category, Acta Univ. Carolin. Math. Phys., 39 (1998), 93–97.
  • J.B. Brown, H. Elalaoui-Talibi, Marczewski-Burstin like characterizations of $\sigma$-algebras, ideals, and measurable functions, Colloq. Math., 82 (1999), 227–286.
  • C. Burstin, Eigenschaften messbarer und nichtmessbarer Mengen, Sitzungsber. Kaiserlichen Akad. Wiss. Math.-Natur. Kl. Abteilung IIa, 123 (1914), 1525–1551.
  • K. Ciesielski, Set Theory for the Working Mathematician,
  • K. Ciesielski, J. Jasinski, Topologies making a given ideal nowhere dense or meager, Topology Appl. 63 (1995), 277–298.
  • E. Marczewski (Szpilrajn), Sur un classe de fonctions de M. Sierpiński et la classe correspondante d'ensembles, Fund. Math., 24 (1935), 17–34.
  • P. Reardon, Ramsey, Lebesgue and Marczewski sets and the Baire property, Fund. Math., 149 (1996), 191–203.
  • K. Schilling, Some category bases which are equivalent to topologies, Real Anal. Exchange, 14(1) (1988–89), 210–214.