Displaying similar documents to “Possibly there is no uniformly completely Ramsey null set of size 2 ω ”

Covering Property Axiom C P A c u b e and its consequences

Krzysztof Ciesielski, Janusz Pawlikowski (2003)

Fundamenta Mathematicae

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We formulate a Covering Property Axiom C P A c u b e , which holds in the iterated perfect set model, and show that it implies easily the following facts. (a) For every S ⊂ ℝ of cardinality continuum there exists a uniformly continuous function g: ℝ → ℝ with g[S] = [0,1]. (b) If S ⊂ ℝ is either perfectly meager or universally null then S has cardinality less than . (c) cof() = ω₁ < , i.e., the cofinality of the measure ideal is ω₁. (d) For every uniformly bounded sequence ⟨ f ₙ ∈ ℝ ℝ ⟩ n < ω of Borel functions...

Monotonically normal e -separable spaces may not be perfect

John E. Porter (2018)

Commentationes Mathematicae Universitatis Carolinae

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A topological space X is said to be e -separable if X has a σ -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that e -separable PIGO spaces are perfect and asked if e -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of e -separable monotonically normal spaces which are not perfect. Extremely normal e -separable spaces are shown to be stratifiable.

Indestructible colourings and rainbow Ramsey theorems

Lajos Soukup (2009)

Fundamenta Mathematicae

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We show that if a colouring c establishes ω₂ ↛ [(ω₁:ω)]² then c establishes this negative partition relation in each Cohen-generic extension of the ground model, i.e. this property of c is Cohen-indestructible. This result yields a negative answer to a question of Erdős and Hajnal: it is consistent that GCH holds and there is a colouring c:[ω₂]² → 2 establishing ω₂ ↛ [(ω₁:ω)]₂ such that some colouring g:[ω₁]² → 2 does not embed into c. It is also consistent that 2 ω ₁ is arbitrarily large,...

A new Lindelöf space with points G δ

Alan S. Dow (2015)

Commentationes Mathematicae Universitatis Carolinae

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We prove that ♦ * implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality 2 ℵ 1 which has points G δ . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.

Axiom T D and the Simmons sublocale theorem

Jorge Picado, Aleš Pultr (2019)

Commentationes Mathematicae Universitatis Carolinae

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More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom T D for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result....