All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 22 Next

Displaying 421 – 440 of 1234

Showing per page

Fundamental groups of one-dimensional spaces

Gerhard Dorfer, Jörg M. Thuswaldner, Reinhard Winkler (2013)

Fundamenta Mathematicae

Let X be a metrizable one-dimensional continuum. We describe the fundamental group of X as a subgroup of its Čech homotopy group. In particular, the elements of the Čech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental group is used to give a new algebro-combinatorial proof of a result due to Eda on continuity properties of homomorphisms from...

Generalized analytic spaces, completeness and fragmentability

Petr Holický (2001)

Czechoslovak Mathematical Journal

Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric.

Generalized Helly spaces, continuity of monotone functions, and metrizing maps

Lech Drewnowski, Artur Michalak (2008)

Fundamenta Mathematicae

Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes...

Generalized linearly ordered spaces and weak pseudocompactness

Oleg Okunev, Angel Tamariz-Mascarúa (1997)

Commentationes Mathematicae Universitatis Carolinae

A space X is truly weakly pseudocompact if X is either weakly pseudocompact or Lindelöf locally compact. We prove that if X is a generalized linearly ordered space, and either (i) each proper open interval in X is truly weakly pseudocompact, or (ii) X is paracompact and each point of X has a truly weakly pseudocompact neighborhood, then X is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].

Hereditarily indecomposable inverse limits of graphs

K. Kawamura, H. M. Tuncali, E. D. Tymchatyn (2005)

Fundamenta Mathematicae

We prove the following theorem: Let G be a compact connected graph and let f: G → G be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum A of G, there is a positive integer n such that fⁿ(A) = G. Then, for each ε > 0, there is a map f ε : G → G which is ε-close to f such that the inverse limit ( G , f ε ) is hereditarily indecomposable.

Hereditarily weakly confluent induced mappings are homeomorphisms

Janusz Charatonik, Włodzimierz Charatonik (1998)

Colloquium Mathematicae

For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.

Homeomorphisms of composants of Knaster continua

Sonja Štimac (2002)

Fundamenta Mathematicae

The Knaster continuum K p is defined as the inverse limit of the pth degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer p ≥ 2, all composants of K p having no endpoints are homeomorphic. This generalizes Bandt’s result which concerns the case p = 2.

Homeomorphisms of inverse limit spaces of one-dimensional maps

Marcy Barge, Beverly Diamond (1995)

Fundamenta Mathematicae

We present a new technique for showing that inverse limit spaces of certain one-dimensional Markov maps are not homeomorphic. In particular, the inverse limit spaces for the three maps from the tent family having periodic kneading sequence of length five are not homeomorphic.

Currently displaying 421 – 440 of 1234