The structure of atoms (hereditarily indecomposable continua)

R. Ball; J. Hagler; Yaki Sternfeld

Displaying similar documents to “The structure of atoms (hereditarily indecomposable continua)”

Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum

Paul Fabel (1998)

Fundamenta Mathematicae

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We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space $l_{2}$ .

From Newton’s method to exotic basins Part I: The parameter space

Krzysztof Barański (1998)

Fundamenta Mathematicae

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This is the first part of the work studying the family $𝔉$ of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of $𝔉$ and give a detailed study of the subfamily $ℱ_{2}$ consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in $ℱ_{2}$ from Newton maps to maps with so-called exotic basins.

Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1

Saharon Shelah, Oren Kolman (1996)

Fundamenta Mathematicae

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We assume a theory T in the logic $L_{κ ω}$ is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.

The Arkhangel’skiĭ–Tall problem: a consistent counterexample

Gary Gruenhage, Piotr Koszmider (1996)

Fundamenta Mathematicae

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We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in ${[ω]}^{ω}$ , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.

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.

Subcontinua of inverse limit spaces of unimodal maps

Karen Brucks, Henk Bruin (1999)

Fundamenta Mathematicae

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We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal...

The Conley index for decompositions of isolated invariant sets

Andrzej Szymczak (1995)

Fundamenta Mathematicae

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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 relative coincidence Nielsen number

Jerzy Jezierski (1996)

Fundamenta Mathematicae

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We define a relative coincidence Nielsen number $N_{r e l} (f, g)$ for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing $N_{r e l} (f, g)$ by the ordinary Nielsen numbers.

Concordant sequences and integral-valued entire functions

Jonathan Pila, Fernando Rodriguez Villegas (1999)

Acta Arithmetica

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A classic theorem of Pólya shows that the function $2^{z}$ is the “smallest” integral-valued entire transcendental function. A variant due to Gel’fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin’s result together with a further generalization.

Classical-type characterizations of non-metrizable ANE(n)-spaces

Valentin Gutev, Vesko Valov (1994)

Fundamenta Mathematicae

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The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is $L C^{n - 1} C^{n - 1}$ (resp., $L C^{n - 1}$ ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

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 $ℝ^{n}$ , we are led to an integration process over quite general sets $A \subseteq q ℝ^{n}$ 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.