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Tytuł artykułu

The sequential topology on complete Boolean algebras

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Abstrakty
EN
We investigate the sequential topology $τ_{s}$ on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the space $(B,τ_{s})$ is Hausdorff. We also characterize sequential cardinals.
Twórcy
  • Mathematical Institute of the Academy of Sciences of Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic, balcar@mbox.cesnet.cz
Bibliografia
  • [AnCh] M. Antonovskiĭ and D. Chudnovsky, Some questions of general topology and Tikhonov semifields II, Russian Math. Surveys 31 (1976), 69-128.
  • [BlJe] A. Blass and T. Jech, On the Egoroff property of pointwise convergent sequences of functions, Proc. Amer. Math. Soc. 98 (1986), 524-526.
  • [En] R. Engelking, General Topology, 2nd ed., PWN, Warszawa, 1985.
  • [Fr0] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984.
  • [Fr1] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, Vol. 3, J. D. Monk and R. Bonnet (eds.), North-Holland, Amsterdam, 1989, 877-980.
  • [Fr2] D. H. Fremlin, Real-valued measurable cardinals, in: Set Theory of the Reals, H. Judah (ed.), Amer. Math. Soc., 1993, 151-304.
  • [Gł] W. Główczyński, Measures on Boolean algebras, Proc. Amer. Math. Soc. 111 (1991), 845-849.
  • [HeRo] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Springer, 1963.
  • [Je] T. Jech, Set Theory, Academic Press, 1978.
  • [KeTa] H. J. Keisler and A. Tarski, From accessible to inaccessible cardinals, Fund. Math. 53 (1964), 225-308.
  • [Ke] J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165-1177.
  • [Ko] S. Koppelberg, General Theory of Boolean Algebras, Vol. 1 of Handbook of Boolean Algebras, J. D. Monk and R. Bonnet (eds.), North-Holland, Amsterdam, 1989.
  • [Ma] D. Maharam, An algebraic characterization of measure algebras, Ann. of Math. 48 (1947), 154-167.
  • [Na] K. Namba, Independence proof of $(ω,ω_1)$-WDL from (ω,ω)-WDL, Comment. Math. Univ. St. Paul. 21 (2) (1972), 47-53.
  • [Pl] G. Plebanek, Remarks on measurable Boolean algebras and sequential cardinals, Fund. Math. 143 (1993), 11-22.
  • [Pr] K. Prikry, On σ-complete prime ideals in Boolean algebras, Colloq. Math. 22 (1971), 209-214.
  • [Ro] F. Rothberger, On families of real functions with a denumerable base, Ann. of Math. 45 (1944), 397-406.
  • [To] S. Todorčević, Some partitions of three-dimensional combinatorial cubes, J. Combin. Theory Ser. A 68 (1994), 410-437.
  • [Tr] V. Trnková, Non-F-topologies, PhD thesis, Prague, 1961 (in Czech).
  • [Vl] D. A. Vladimirov, Boolean Algebras, Nauka, Moscow, 1969 (in Russian).
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv155i1p59bwm
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