Beyond Lebesgue and Baire II: Bitopology and measure-category duality
نویسندگان
چکیده
منابع مشابه
Bitopology and measure-category duality
We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density toplologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on in nitary combinatorics due to Kestelman and to Borwein and Ditor. As a by-product we give a uni ed proof of the measure and category cases of Unif...
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The existence of such a function is independent from ZFC. Recall that for an ideal I, we define non(I) = min{|X| : X 6∈ I}. The following fact shows that it is consistent that an Erdös – Sierpiński mapping does not exist: Theorem 1.3 (see [1]). It is consistent that non(M) 6= non(N ). An Erdös–Sierpiński mapping is an isomorphism of the structures 〈R,N〉 and 〈R,M〉 and thus preserves basic set-th...
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We show that there is no Erdös–Sierpiński mapping preserving addition. Let M and N be the ideals of meager and null subsets of 2. Definition 1. A bijection F : 2 −→ 2 is called Erdös–Sierpiński mapping if X ∈ N ⇐⇒ F [X ] ∈ M and X ∈ M ⇐⇒ F [X ] ∈ N . Theorem 2 ([4], [1]). Assume CH. There exists an Erdös–Sierpiński mapping. Since the existence of Erdös–Sierpiński mapping implies that the ideals...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2010
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm121-2-5