Attractors and Inverse Limits.
This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.
Au bord de certains polyèdres hyperboliques
Le cadre de cet article est celui des groupes et des espaces hyperboliques de M. Gromov. Il est motivé par la question suivante : comment différencier deux groupes hyperboliques à quasi-isométrie près ? On illustre ce problème en détaillant un exemple de M. Gromov issu de Asymptotic invariants for infinite groups. On décrit une famille infinie de groupes hyperboliques, deux à deux non quasi-isométriques, de bord la courbe de Menger. La méthode consiste à étudier leur structure quasi-conforme au...
Aull-paracompactness and strong star-normality of subspaces in topological spaces
We prove for a subspace of a -space , is (strictly) Aull-paracompact in and is Hausdorff in if and only if is strongly star-normal in . This result provides affirmative answers to questions of A.V. Arhangel’skii–I.Ju. Gordienko [3] and of A.V. Arhangel’skii [2].
AUnif: A common supercategory of pMET and Unif.
Autohomeomorphism groups of spaces with unique non-isolated point
Automata, Borel functions and real numbers in Pisot base
This note is about functions ƒ : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A x B. These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such function are continuous or not. In 1920 W. Sierpinski showed that a function is Baire class 1 if and only if both the overgraph and the undergraph of f are Fσ. We show that such characterization is also true for functions on infinite words if we replace the real...
Automorphism groups of complements of points
Automorphism invariants for semigroups.
Automorphisms and subsystems of the shift.
Averages of quasi-continuous functions
The goal of this paper is to characterize the family of averages of comparable (Darboux) quasi-continuous functions.
Axiom systems for Lipschitz structures
Axiom and the Simmons sublocale theorem
More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result. In this...
Axioms weaker then
on spaces of homogeneous type: a density result on - spaces.
Bad Wadge-like reducibilities on the Baire space
We consider various collections of functions from the Baire space into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of...
Baire category from an abstract viewpoint
Baire category in spaces of probability measures
Baire category in spaces of probability measures, II
Baire category results for quasi–copulas
The aim of this manuscript is to determine the relative size of several functions (copulas, quasi– copulas) that are commonly used in stochastic modeling. It is shown that the class of all quasi–copulas that are (locally) associated to a doubly stochastic signed measure is a set of first category in the class of all quasi– copulas. Moreover, it is proved that copulas are nowhere dense in the class of quasi-copulas. The results are obtained via a checkerboard approximation of quasi–copulas.
Baire class of completely additive systems of Baire sets