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Showing papers in "Topology and its Applications in 2007"


Journal ArticleDOI
TL;DR: A fuzzy quasi-metric version of the Banach contraction principle constitutes an extension of the famous Grabiec fixed point theorem and is applied to deduce the existence of solution for some recurrence equations associated to the analysis of Quicksort algorithms and Divide & Conquer algorithms, respectively.

76 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the classes of compact, countably compact, and pseudocompact spaces are self-dual with respect to neighbourhood assignments, and that all spaces dual to hereditarily Lindelof spaces are Lindelhof spaces.

76 citations


Journal ArticleDOI
Eli Glasner1
TL;DR: A survey of the theory of enveloping semigroups in topological dynamics can be found in this paper, where the authors review the existing classical theory of envelope groups, due mainly to Robert Ellis, and then proceed to describe some new connections which were discovered in the last few years between three seemingly unrelated theories: enveloping semiigroups, chaotic behavior, and representation of dynamical systems on Banach spaces.

73 citations


Journal ArticleDOI
TL;DR: In this article, the geometry of B-manifolds is studied, and some properties of Riemannian curvature tensors of paraholomorphic B-mansifolds are given.

66 citations


Journal ArticleDOI
TL;DR: In this paper, a generalized covering space theory for a class of uniform spaces called coverable spaces is developed, including all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular Peano continua, as well as more pathological spaces like the topologist's sine curve.

56 citations


Journal ArticleDOI
TL;DR: An Arzela-Ascoli theorem for asymmetric metric spaces is proved in this article, and one genuinely asymmetric condition is introduced, and it is shown that several classic statements fail in the asymmetric context if this assumption is dropped.

53 citations


Journal ArticleDOI
Masami Sakai1

51 citations


Journal ArticleDOI
TL;DR: This work introduces a novel strand-passage algorithm which generates a Markov chain in knot space and investigates transition probabilities between knots, using the BFACF algorithm to generate ensembles of polygons in Z(3) of fixed knot type.

45 citations


Journal ArticleDOI
TL;DR: In this paper, the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the categories of (uncertainty-free) metric spaces, and uniform maps, is studied.

42 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that compact homogeneity is the strongest homogeneity property possible in the Urysohn space U and its isometry group, and that any Polish metric space is isometric to the set of fixed points of some isometry φ.

42 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the kneading sequence theory of maps on dendrites, concentrating on those maps having one "turning point" and the unique itinerary property (i.e., distinct points have distinct itineraries).

Journal ArticleDOI
TL;DR: In this paper, the authors introduce mathematicians to a cash-in-advance model from economics and show that tools from inverse limits and dynamical systems developed in the last forty or so years are applicable to it.

Journal ArticleDOI
TL;DR: In this article, it was shown that the results of Tkachenko, Tomita and Watson are compatible with the total failure of Martin's Axiom and the existence of a Wallace semigroup under CH.

Journal ArticleDOI
TL;DR: In this paper, it was shown that hyperbolic structures and spherical CR structures on a 3D manifold are contained in fixed point sets of a larger class of structures associated to a triangulation of the manifold.

Journal ArticleDOI
TL;DR: In this paper, it was shown that a normal topological space X is a QN-space if and only if X has the property S1(Γshr,Γ ).

Journal ArticleDOI
TL;DR: In this paper, the authors studied a family of rational maps acting on the Riemann sphere with a single preperiodic critical orbit and provided a complete topological description of their Julia sets.

Journal ArticleDOI
TL;DR: In this paper, the p-adic framed braid group F ∞, n, arising as the inverse limit of the modular framed braids, is defined and approximated.

Journal ArticleDOI
TL;DR: In this article, it was shown that every P-chaotic map from a continuous space to itself is chaotic in the sense of Devaney and exhibits distributional chaos of type 1 with positive topological entropy.

Journal ArticleDOI
TL;DR: In this article, the authors study twentynine equivalent characterisations for a metric space to have an Atsuji completion, and show that all of them are equivalent to the characterisation in this paper.

Journal ArticleDOI
TL;DR: The isometry group Iso (U ) of the universal Urysohn metric space U equipped with the natural Polish topology is a Levy group in the sense of Gromov and Milman, that is, admits an approximating chain of compact subgroups as discussed by the authors.

Journal ArticleDOI
TL;DR: Dranishnikov et al. as discussed by the authors showed that the asymptotic Assouad-Nagata dimension of a metric space X coincides with the covering dimension of the Higson corona of a sublinear coarse structure on X.

Journal ArticleDOI
TL;DR: In this article, the Edelstein result for contractive mappings is extended to Hausdorff (not necessarily completely regular) topological spaces and generalized in many aspects, including the existence of fixed points.

Journal ArticleDOI
TL;DR: Henriksen and Isbell as mentioned in this paper showed that if a compact Hausdorff space X is first countable at least at one point, and X can be represented as the union of two complementary dense subspaces Y and Z, each of which is homeomorphic to a topological group (not necessarily the same), then X is separable and metrizable.

Journal ArticleDOI
TL;DR: This paper designs an combinatorial multivalued approximation from a simplicial decomposition of the phase space, which can be used to extract isolating blocks for isolated invariant sets and obtains local conditions on the underlying simplicial approximation that guarantees that the chain recurrent set can be well-approximated.

Journal ArticleDOI
Erik Palmgren1
TL;DR: In this article, a full and faithful functor M from locally compact metric spaces and continuous functions into the category of formal topol functions has been established, within constructive mathematics, which is similar to the one we consider in this paper.

Journal ArticleDOI
TL;DR: In this paper, simplicial cochains of a triangulated manifold were developed and proved to converge to their differential-geometric analogues as the triangulation becomes small.

Journal ArticleDOI
TL;DR: In this paper, a general method of construction of such an extension of a T 0 -space is worked out and it is finally shown that under certain condition imposed on the ideals involved, the said extension space turns out to be the compactification of a given space.

Journal ArticleDOI
TL;DR: In this article, the authors continue the study of bitopological separation axioms, and introduce two concepts of pairwise Lindelof spaces and the properties for them are established.

Journal ArticleDOI
TL;DR: In this article, Menger-bounded and Rothberger bounded groups were examined in terms of measure-theoretic properties relative to left-invariant metrics and games.

Journal ArticleDOI
TL;DR: For a Tychonoff space X, the authors showed that (USC(X) and C(X)) are homeomorphic to the Hilbert cube if and only if X is an infinite compact metric space and the set of isolated points is not dense in X.