Displaying similar documents to “Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum”

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.

The structure of atoms (hereditarily indecomposable continua)

R. Ball, J. Hagler, Yaki Sternfeld (1998)

Fundamenta Mathematicae

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Let X be an atom (= hereditarily indecomposable continuum). Define a metric ϱ on X by letting ϱ ( x , y ) = W ( A x y ) where A x , y is the (unique) minimal subcontinuum of X which contains x and y and W is a Whitney map on the set of subcontinua of X with W(X) = 1. We prove that ϱ is an ultrametric and the topology of (X,ϱ) is stronger than the original topology of X. The ϱ-closed balls C(x,r) = y ∈ X:ϱ ( x,y) ≤ r coincide with the subcontinua of X. (C(x,r) is the unique subcontinuum of X which contains x and has...

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...

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.

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.

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.

Postnikov invariants of H-spaces

Dominique Arlettaz, Nicole Pointet-Tischler (1999)

Fundamenta Mathematicae

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It is known that the order of all Postnikov k-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the k-invariants k m + 1 ( X ) of X in dimensions m ≤ 2n if X is an (n-1)-connected H-space which is not necessarily of finite type (n ≥ 1). Similar results hold more generally for higher k-invariants if X is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of X.