The Arrow-Hahn Construction in a Locally Compact Metric Space

2020 ◽  
pp. 281-299
Author(s):  
Douglas S. Bridges
Keyword(s):  
Metric Space ◽  
Locally Compact ◽  
Compact Metric Space

Horseshoes and the Conley index spectrum

2000 ◽  
Vol 20 (2) ◽  
pp. 365-377 ◽  
Author(s):  
MARIA C. CARBINATTO ◽  
JAROSLAW KWAPISZ ◽  
KONSTANTIN MISCHAIKOW
Keyword(s):  
Metric Space ◽  
Conley Index ◽  
Spectral Information ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Continuous Map ◽  
Full Shift ◽  
Shift Dynamics ◽  
Isolating Neighborhood

Given a continuous map on a locally compact metric space and an isolating neighborhood which is decomposed into two disjoint isolating neighborhoods, it is shown that the spectral information of the associated Conley indices is sufficient to conclude the existence of a semi-conjugacy onto the full shift dynamics on two symbols.

A Denoised Version of Some Kinds of Set Convergence

2005 ◽  
Vol 5 (3) ◽  
Author(s):  
Filomena A. Lops
Keyword(s):  
Hausdorff Measure ◽  
Metric Space ◽  
Lower Semicontinuity ◽  
Set Convergence ◽  
Minimizing Sequence ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Compactness Result ◽  
Hausdorff Convergence ◽  
Kuratowski Convergence

AbstractThe aim of this paper consists of introducing on a locally compact and σ-compact metric space a notion of set convergence, which generalizes the Hausdorff convergence, the local Hausdorff convergence and the Kuratowski convergence. We analyze the connections beetwen the three new notions: and. in particular, we prove a compactness result. As a first application of this convergence we give, on a sequence of sets, a condition which assures the lower semicontinuity of the Hausdorff measure with respect to this new convergence and we show that this condition is satisfied by any minimizing sequence of Mumford-Shah functional.

scholarly journals Regional topology and approximative solutions of difference and differential equations

2015 ◽  
Vol 63 (1) ◽  
pp. 183-203 ◽  
Author(s):  
Janusz Migda
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Point Theorem ◽  
Metric Space ◽  
Schauder’S Fixed Point Theorem ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Real Functions

Abstract We introduce a topology, which we call the regional topology, on the space of all real functions on a given locally compact metric space. Next we obtain new versions of Schauder’s fixed point theorem and Ascoli’s theorem. We use these theorems and the properties of the iterated remainder operator to establish conditions under which there exist solutions, with prescribed asymptotic behaviour, of some difference and differential equations.

Character Amenability of Lipschitz Algebras

2014 ◽  
Vol 57 (1) ◽  
pp. 37-41 ◽  
Author(s):  
Mahshid Dashti ◽  
Rasoul Nasr-Isfahani ◽  
Sima Soltani Renani
Keyword(s):  
Metric Space ◽  
Banach Algebras ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Character Amenability

AbstractLet be a locally compact metric space and let 𝒜 be any of the Lipschitz algebras , , or . In this paper, we show, as a consequence of rather more general results on Banach algebras, that 𝒜 is C-character amenable if and only if is uniformly discrete.

scholarly journals On the uniform exponential stability of linear skew-product semiflows

2006 ◽  
Vol 4 (2) ◽  
pp. 145-161
Author(s):  
Ciprian Preda
Keyword(s):  
Exponential Stability ◽  
Large Class ◽  
Metric Space ◽  
Orlicz Spaces ◽  
Skew Product ◽  
Test Functions ◽  
Type Condition ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Uniform Exponential Stability

The problem of uniform exponential stability of linear skew-product semiflows on locally compact metric space with Banach fibers, is discussed. It is established a connection between the uniform exponential stability of linear skewproduct semiflows and some admissibility-type condition. This approach is based on the method of “test functions”, using a very large class of function spaces, the so-called Orlicz spaces.

scholarly journals Attractors of dynamical systems in locally compact spaces

2019 ◽  
Vol 17 (1) ◽  
pp. 465-471 ◽  
Author(s):  
Gang Li ◽  
Yuxia Gao
Keyword(s):  
Dynamical Systems ◽  
Metric Space ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Compact Spaces ◽  
Isolating Block ◽  
Locally Compact Spaces

Abstract In this article the properties of attractors of dynamical systems in locally compact metric space are discussed. Existing conditions of attractors and related results are obtained by the near isolating block which we present.

Perfect Images of Zero-Dimensional Separable Metric Spaces

1982 ◽  
Vol 25 (1) ◽  
pp. 41-47 ◽  
Author(s):  
Jan Van Mill ◽  
R. Grant Woods
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Dense Subset ◽  
Cantor Set ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Continuous Surjection

AbstractLet Q denote the rationals, P the irrationals, C the Cantor set and L the space C − {p} (where p ∈ C). Let f : X → Y be a perfect continuous surjection. We show: (1) If X ∈ {Q, P, Q × P}, or if f is irreducible and X ∈ {C, L}, then Y is homeomorphic to X if Y is zero-dimensional. (2) If X ∈ {P, C, L} and f is irreducible, then there is a dense subset S of Y such that f|f ← [S] is a homeomorphism onto S. However, if Z is any σ-compact nowhere locally compact metric space then there is a perfect irreducible continuous surjection from Q × C onto Z such that each fibre of the map is homeomorphic to C.

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