Displaying similar documents to “Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary.”

The box-counting dimension for geometrically finite Kleinian groups

B. Stratmann, Mariusz Urbański (1996)

Fundamenta Mathematicae

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We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide...

The geometry of laminations

Robbert Fokkink, Lex Oversteegen (1996)

Fundamenta Mathematicae

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A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.

Compositions of simple maps

Jerzy Krzempek (1999)

Fundamenta Mathematicae

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A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple.  Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails...

Reverse mathematics of some topics from algorithmic graph theory

Peter Clote, Jeffry Hirst (1998)

Fundamenta Mathematicae

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This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.

Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Andrei Sivak (1996)

Fundamenta Mathematicae

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We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in ℝ n , n ≥ 1, is a σ-limit set for some continuous map.

Are initially ω 1 -compact separable regular spaces compact?

Alan Dow, Istvan Juhász (1997)

Fundamenta Mathematicae

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We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.

A Ramsey theorem for polyadic spaces

Murray Bell (1996)

Fundamenta Mathematicae

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A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that ( α κ ) ω is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin...

Connected covers and Neisendorfer's localization theorem

C. McGibbon, J. Møller (1997)

Fundamenta Mathematicae

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Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann...

Period doubling, entropy, and renormalization

Jun Hu, Charles Tresser (1998)

Fundamenta Mathematicae

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We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.