Displaying similar documents to “For almost every tent map, the turning point is typical”

The Zahorski theorem is valid in Gevrey classes

Jean Schmets, Manuel Valdivia (1996)

Fundamenta Mathematicae

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Let Ω,F,G be a partition of n such that Ω is open, F is F σ and of the first category, and G is G δ . We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.

Spaces of upper semicontinuous multi-valued functions on complete metric spaces

Katsuro Sakai, Shigenori Uehara (1999)

Fundamenta Mathematicae

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Let X = (X,d) be a metric space and let the product space X × ℝ be endowed with the metric ϱ ((x,t),(x’,t’)) = maxd(x,x’), |t - t’|. We denote by U S C C B ( X ) the space of bounded upper semicontinuous multi-valued functions φ : X → ℝ such that each φ(x) is a closed interval. We identify φ U S C C B ( X ) with its graph which is a closed subset of X × ℝ. The space U S C C B ( X ) admits the Hausdorff metric induced by ϱ. It is proved that if X = (X,d) is uniformly locally connected, non-compact and complete, then U S C C B ( X ) is homeomorphic...

Property C'', strong measure zero sets and subsets of the plane

Janusz Pawlikowski (1997)

Fundamenta Mathematicae

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Let X be a set of reals. We show that  • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections F x (x ∈ X) null, x X F x is null;  • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections F x (x ∈ ℝ) null, x X F x is null.

A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary

W. Jurkat, D. Nonnenmacher (1994)

Fundamenta Mathematicae

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Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in n , we are led to an integration process over quite general sets A q n with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form.

Dugundji extenders and retracts on generalized ordered spaces

Gary Gruenhage, Yasunao Hattori, Haruto Ohta (1998)

Fundamenta Mathematicae

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For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an L c h -extender (resp. L c c h -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous L c h -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology...

Homotopy orbits of free loop spaces

Marcel Bökstedt, Iver Ottosen (1999)

Fundamenta Mathematicae

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Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors Ω λ ( R ) and ℓ(R) together with algebra homomorphisms e : Ω λ ( R ) H * ( Λ X ) and ψ : ( R ) H * ( E S 1 × S 1 Λ X ) . When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.

An ordinal version of some applications of the classical interpolation theorem

Benoît Bossard (1997)

Fundamenta Mathematicae

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Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space E 1 with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space E 2 with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of E 1 and E 2 can be controlled by the Szlenk index of E, where the...

The universal functorial Lefschetz invariant

Wolfgang Lück (1999)

Fundamenta Mathematicae

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We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and L 2 -torsion of mapping tori. We examine its behaviour under fibrations.

Construction of non-subadditive measures and discretization of Borel measures

Johan Aarnes (1995)

Fundamenta Mathematicae

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The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is shown that “discretization” of ordinary measures is possible in the following sense. Given a positive regular Borel measure λ, one may construct a sequence of non-subadditive measures μ n , each of which only takes a finite set of values, and such that μ n converges to λ in the w*-topology. ...

Operators on C(ω^α) which do not preserve C(ω^α)

Dale Alspach (1997)

Fundamenta Mathematicae

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It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from C ( ω ω α ) onto itself such that if Y is a subspace of C ( ω ω α ) which is isomorphic to C ( ω ω α ) , then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from C ( ω ω α ) onto itself there is a subspace of C ( ω ω α ) which is isomorphic to C ( ω ω α ) on which the operator is an isomorphism.

A partial order where all monotone maps are definable

Martin Goldstern, Saharon Shelah (1997)

Fundamenta Mathematicae

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It is consistent that there is a partial order (P,≤) of size 1 such that every monotone function f:P → P is first order definable in (P,≤).

Normal subspaces in products of two ordinals

Nobuyuki Kemoto, Tsugunori Nogura, Kerry Smith, Yukinobu Yajima (1996)

Fundamenta Mathematicae

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Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of ( λ + 1 ) 2 .

Computing Reidemeister classes

Davide Ferrario (1998)

Fundamenta Mathematicae

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In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group π 1 ( X ) need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.

Cantor manifolds in the theory of transfinite dimension

Wojciech Olszewski (1994)

Fundamenta Mathematicae

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For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space Z α such that i n d Z α = α , and no closed subset L of Z α with ind L less than the predecessor of α is a partition in Z α . An α-dimensional Cantor Ind-manifold can be constructed similarly.

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 .

A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

Witold Marciszewski (1997)

Fundamenta Mathematicae

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We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions c p ( X ) onto c p ( X ) × ℝ . I n p a r t i c u l a r , cp(X) i s n o t l i n e a r l y h o m e o m o r p h i c t o cp(X) × . One of these examples is compact. This answers some questions of Arkhangel’skiĭ.