Metric spaces with asymptotic property C and finite decomposition complexity

We introduce the asymptotic property associated with recurrence-like behavior of orbits in dynamical systems in general metric spaces. We define a notion of weak asymptotic periodicity and determine its elementary properties and relations including the invariance by topological conjugacy. We use the equicontinuity and the topology of the space to describe necessary and sufficient conditions for the existence of such a behavior.

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Operator norm localization property of metric spaces under finite decomposition complexity

Journal of Functional Analysis ◽

10.1016/j.jfa.2009.05.022 ◽

2009 ◽

Vol 257 (9) ◽

pp. 2938-2950 ◽

Cited By ~ 3

Author(s):

Xiaoman Chen ◽

Qin Wang ◽

Xianjin Wang

Keyword(s):

Metric Spaces ◽

Operator Norm ◽

Localization Property ◽

Decomposition Complexity

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On the stability of asymptotic property C for products and some group extensions

Algebraic & Geometric Topology ◽

10.2140/agt.2018.18.221 ◽

2018 ◽

Vol 18 (1) ◽

pp. 221-245 ◽

Cited By ~ 3

Author(s):

Gregory Bell ◽

Andrzej Nagórko

Keyword(s):

Asymptotic Property ◽

Group Extensions ◽

The Stability ◽

Asymptotic Property C

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Decomposition theorems for asymptotic property C and property A

Topology and its Applications ◽

10.1016/j.topol.2019.02.013 ◽

2019 ◽

Vol 256 ◽

pp. 248-261 ◽

Cited By ~ 1

Author(s):

G. Bell ◽

D. Głodkowski ◽

A. Nagórko

Keyword(s):

Asymptotic Property ◽

Property A ◽

Decomposition Theorems ◽

Asymptotic Property C

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Crystallography in two-dimensional metric spaces*

Zeitschrift für Kristallographie ◽

10.1524/zkri.1969.130.1-6.277 ◽

1969 ◽

Vol 130 (1-6) ◽

pp. 277-303 ◽

Cited By ~ 6

Author(s):

Aloysio Janner ◽

Edgar Ascher

Keyword(s):

Metric Spaces ◽

Two Dimensional

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Convergence and Stability For Ishikawa Iterative Scheme in Convex Metric Spaces

Indian Journal Of Applied Research ◽

10.15373/2249555x/june2014/104 ◽

2011 ◽

Vol 4 (6) ◽

pp. 341-343

Author(s):

Aarti Kadian ◽

◽

Alok Kumar

Keyword(s):

Metric Spaces ◽

Iterative Scheme ◽

Convergence And Stability ◽

Convex Metric Spaces

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Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2017.1.2 ◽

2016 ◽

Vol 2017 (1) ◽

pp. 17-30 ◽

Cited By ~ 22

Author(s):

Muhammad Usman Ali ◽

◽

Tayyab Kamran ◽

Mihai Postolache ◽

◽

...

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Spaces ◽

Integral Inclusion

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ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.37.2001.1-2.9 ◽

2001 ◽

Vol 37 (1-2) ◽

pp. 169-184

Author(s):

B. Windels

Keyword(s):

Metric Spaces ◽

Uniform Spaces ◽

Complete Metric Spaces ◽

The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

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