Some remarks about Mycielski ideals
Shizuo Kamo (1993)
Colloquium Mathematicae
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Shizuo Kamo (1993)
Colloquium Mathematicae
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Marinari, Maria Grazia, Ramella, Luciana (2006)
Beiträge zur Algebra und Geometrie
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Saharon Shelah (2000)
Fundamenta Mathematicae
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We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.
Andrzej Nowik (1999)
Colloquium Mathematicae
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We prove some properties of uniformly completely Ramsey null sets (for example, every hereditarily Menger set is uniformly completely Ramsey null).
J. Barnett (1992)
Fundamenta Mathematicae
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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...
Michał Morayne (1992)
Fundamenta Mathematicae
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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Benjamin, E., Bresinsky, H. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Saharon Shelah (2000)
Fundamenta Mathematicae
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The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants. ...
Udayan Darji (1993)
Colloquium Mathematicae
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Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...
Moreno-Socías, Guillermo, Snellman, Jan (2002)
Homology, Homotopy and Applications
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