Strong meager properties for filters

Claude Laflamme

Displaying similar documents to “Strong meager properties for filters”

Filters and sequences

Sławomir Solecki (2000)

Fundamenta Mathematicae

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We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a $Π_{3}^{0}$ filter is itself $Π_{3}^{0}$ and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou’s...

Classification of function spaces with the pointwise topology determined by a countable dense set

Tadeusz Dobrowolski, Witold Marciszewski (1995)

Fundamenta Mathematicae

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Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?

Valentin Gutev, Haruto Ohta (2000)

Fundamenta Mathematicae

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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.

Combinatorics of open covers (III): games, Cp (X)

Marion Scheepers (1997)

Fundamenta Mathematicae

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Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces $C_{p} (X)$ of countable tightness, give new characterizations of countable fan tightness and countable strong fan tightness. In particular, each of these properties is characterized by a Ramseyan theorem.

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

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I prove that the statement that “every linear order of size $2^{ω}$ can be embedded in $(ω^{ω}, ≪)$ ” is consistent with MA + ¬ wKH.

The minimum uniform compactification of a metric space

R. Grant Woods (1995)

Fundamenta Mathematicae

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It is shown that associated with each metric space (X,d) there is a compactification $u_{d} X$ of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of $u_{d} X$ are presented, and a detailed study of the structure of $u_{d} X$ is undertaken. This culminates in a topological characterization of the outgrowth $u_{d} ℝ^{n} ∖ ℝ^{n}$ , where $(ℝ^{n}, d)$ is Euclidean n-space with its usual metric. ...

Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group

Bernd Günther, L. Mdzinarishvili (1997)

Fundamenta Mathematicae

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We prove that Alexander-Spanier cohomology $H^{n} (X; G)$ with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.

A Lefschetz-type coincidence theorem

Peter Saveliev (1999)

Fundamenta Mathematicae

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A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_{f g} = λ_{f g}$ , that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_{f g} \neq 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like”...

Properly homotopic nontrivial planes are isotopic

Bobby Winters (1995)

Fundamenta Mathematicae

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It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to $ℝ^{3}$ are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.

Countable Toronto spaces

Gary Gruenhage, J. Moore (2000)

Fundamenta Mathematicae

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A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each $α < ω_{1}$ .

For almost every tent map, the turning point is typical

Henk Bruin (1998)

Fundamenta Mathematicae

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Let $T_{a}$ be the tent map with slope a. Let c be its turning point, and $μ_{a}$ the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, $ʃ g d μ_{a} = l i m_{n \to \infty} \frac{1}{n} \sum_{i = 0}^{n - 1} g (T_{a}^{i} (c))$ . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.

ℳ-rank and meager types

Ludomir Newelski (1995)

Fundamenta Mathematicae

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Assume T is superstable and small. Using the multiplicity rank ℳ we find locally modular types in the same manner as U-rank considerations yield regular types. We define local versions of ℳ-rank, which also yield meager types.