A Metric Space with Transfinite Asymptotic Dimension 2ω + 1

2021 ◽  
Vol 42 (3) ◽  
pp. 357-366
Author(s):  
Yan Wu ◽  
Jingming Zhu
Keyword(s):  
Metric Space ◽  
Asymptotic Dimension

scholarly journals METRIC SPACES WITH SUBEXPONENTIAL ASYMPTOTIC DIMENSION GROWTH

2012 ◽  
Vol 22 (02) ◽  
pp. 1250011 ◽  
Author(s):  
NARUTAKA OZAWA
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Asymptotic Dimension ◽  
Property A

We prove that a metric space with subexponential asymptotic dimension growth has Yu's property A.

scholarly journals Geodesic spaces of low Nagata dimension

2021 ◽  
Vol 47 (1) ◽  
pp. 83-88
Author(s):  
Martina Jørgensen ◽  
Urs Lang
Keyword(s):  
Planar Graph ◽  
Recent Work ◽  
Metric Space ◽  
Three Dimensional ◽  
Asymptotic Dimension ◽  
Hadamard Manifolds ◽  
Continuous Map ◽  
Geodesic Metric Space ◽  
Geodesic Metric ◽  
Nagata Dimension

We show that every geodesic metric space admitting an injective continuous map into the plane as well as every planar graph has Nagata dimension at most two, hence asymptotic dimension at most two. This relies on and answers a question in a recent work by Fujiwara and Papasoglu. We conclude that all three-dimensional Hadamard manifolds have Nagata dimension three. As a consequence, all such manifolds are absolute Lipschitz retracts.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

On Fixed Point Theorems in Complete Metric Space

2019 ◽  
Vol 10 (7) ◽  
pp. 1419-1425
Author(s):  
Jayashree Patil ◽  
Basel Hardan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space
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