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1997 | 153 | 1 | 25-40
Tytuł artykułu

Nonseparable Radon measures and small compact spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube $[0, 1]^κ$ (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ κ this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of $ω_1$ null sets in $2^{ω1}$ such that every perfect set meets one of them, we construct a compact space showing that the answer to the above problem is "no" for κ = ω. We also give alternative proofs of two related results due to Kunen and van Mill [18].
Słowa kluczowe
Rocznik
Tom
153
Numer
1
Strony
25-40
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-05-07
poprawiono
1996-11-14
poprawiono
1997-01-30
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland, grzes@math.uni.wroc.pl
Bibliografia
  • [1] S. Argyros, S. Mercourakis and S. Negrepontis, Functional-analytic properties of Corson-compact spaces, Studia Math. 89 (1988), 197-229.
  • [2] T. Bartoszyński and H. Judah, Set Theory: on the structure of the real line, A. K. Peters, 1995.
  • [3] T. Bartoszyński and S. Shelah, Closed measure zero sets, Ann. Pure Appl. Logic 58 (1992), 93-110.
  • [4] J. Brendle, H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Ann. Pure Appl. Logic 58 (1992), 185-199.
  • [5] J. Cichoń, A. Kamburelis and J. Pawlikowski, On dense subsets of the measure algebra, Proc. Amer. Math. Soc. 94 (1985), 142-146.
  • [6] J. Cichoń, A. Szymański and B. Węglorz, On intersections of sets of positive Lebesgue measure, Colloq. Math. 52 (1987), 173-177.
  • [7] W. W. Comfort and S. Negrepontis, Chain Conditions in Topology, Cambridge Univ. Press, 1982.
  • [8] R. G. Douglas, On extremal measures and subspace density, Michigan Math. J. 11 (1964), 243-246.
  • [9] M. Džamonja and K. Kunen, Measures on compact HS spaces, Fund. Math. 143 (1993), 41-54.
  • [10] M. Džamonja and K. Kunen, Properties of the class of measure separable compact spaces, Fund. Math. 147 (1995), 261-277.
  • [11] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984.
  • [12] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, J. D. Monk (ed.), North-Holland, 1989, Vol. 3, Chap. 22, 877-980.
  • [13] D. H. Fremlin, Real-valued measurable cardinals, in: Israel Math. Conf. Proc. 6, 1993, 961-1044.
  • [14] R. Haydon, On Banach spaces which contain $l^1(τ)$ and types of measures on compact spaces, Israel J. Math. 28 (1977) 313-324.
  • [15] R. Haydon, On dual $L^1$-spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978) 142-152.
  • [16] K. Kunen, Set Theory, Stud. Logic 102, North-Holland, 1980.
  • [17] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287.
  • [18] K. Kunen and J. van Mill, Measures on Corson compact spaces, Fund. Math. 147 (1995), 61-72.
  • [19] G. Plebanek, Compact spaces that result from adequate families of sets, Topology Appl. 65 (1995), 257-270.
  • [20] G. Plebanek, On Radon measures on first-countable spaces, Fund. Math. 148 (1995), 159-164.
  • [21] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa, 1971.
  • [22] B. E. Shapirovskiĭ, Special types of embeddings in Tychonoff cubes. Subspaces of Σ-products and cardinal invariants, in: Á. Császár (ed.), Topology, Vol. II, North-Holand, Amsterdam, 1980, 1055-1086.
  • [23] J. E. Vaughan, Small uncountable cardinals and topology, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, 1990, Chapter 11, 195-216.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-fmv153i1p25bwm
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