Nonseparable Radon measures and small compact spaces

• Autorzy: Grzegorz Plebanek
• 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].

Kategorie tematyczne

• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 153
• Numer: 1
• Strony: 25-40

Daty

wydano

1997

otrzymano

1996-05-07

poprawiono

1996-11-14

poprawiono

1997-01-30

Twórcy

autor

Grzegorz Plebanek

• Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland

Bibliografia

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