Nonpositive curvature is not coarsely universal
Sign Up to like & getrecommendations! Published in 2019 at "Inventiones mathematicae"
DOI: 10.1007/s00222-019-00878-1
Abstract: We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question of Gromov (Geometric group theory, Cambridge University Press, Cambridge, 1993) and is in contrast to… read more here.
Keywords: space; nonpositive curvature; ell infty; metric space ... See more keywords
Extensions of T0-quasi-metrics
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-017-0753-z
Abstract: Let $${(X, m, \leq)}$$(X,m,≤) be a partially ordered metric space, that is, a metric space (X, m) equipped with a partial order $${\leq}$$≤ on X. We say that a T0-quasi-metric d on X is m-splitting… read more here.
Keywords: metric space; partially ordered; ordered metric; quasi metric ... See more keywords
Descriptive set theory for expansive systems
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.12.014
Abstract: Abstract Kato [5] and Artigue [3] merged the theory of expansive systems [10] and foliations with the continuum theory [14] . Here we merge the expansive systems but with the descriptive set theory [6] instead.… read more here.
Keywords: metric space; homeomorphism; meagre expansive; expansive systems ... See more keywords
Strong submeasures and applications to non-compact dynamical systems
Sign Up to like & getrecommendations! Published in 2020 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2020.132
Abstract: A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach… read more here.
Keywords: strong submeasures; strong submeasure; metric space; compact metric ... See more keywords
Existence and Uniqueness of a Common Best Proximity Point on Fuzzy Metric Space
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DOI: 10.1080/16168658.2020.1746484
Abstract: In this paper, first we introduce the notion of proximally weakly compatible mappings and we extend the CLRg property (CLRg-Common limit in the range of g) to the case of non-self mappings. Then we prove… read more here.
Keywords: fuzzy metric; metric space; point; common best ... See more keywords
Structure of plane gravitational waves of nonmetricity in affine-metric space
Sign Up to like & getrecommendations! Published in 2018 at "Classical and Quantum Gravity"
DOI: 10.1088/1361-6382/aace79
Abstract: A definition of an affine-metric space of the plane wave type is given using the analogy with the properties of plane electromagnetic waves in Minkowski space. The action of the Lie derivative on the 40… read more here.
Keywords: space; affine metric; form; metric space ... See more keywords
SCHMIDT'S GAME ON HAUSDORFF METRIC AND FUNCTION SPACES: GENERIC DIMENSION OF SETS AND IMAGES
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DOI: 10.1112/mtk.12068
Abstract: We consider Schmidt's game on the space of compact subsets of a given metric space equipped with the Hausdorff metric, and the space of continuous functions equipped with the supremum norm. We are interested in… read more here.
Keywords: game hausdorff; game; metric space; schmidt game ... See more keywords
On the Metric Space of Closed Subsets of a Metric Space and Set-Valued Maps with Closed Images
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Notes"
DOI: 10.1134/s0001434618070118
Abstract: The space clos(X) of all nonempty closed subsets of an unbounded metric space X is considered. The space clos(X) is endowed with a metric in which a sequence of closed sets converges if and only… read more here.
Keywords: space closed; closed subsets; space; metric space ... See more keywords
Fixed Points of a φ-G-Contractive Mapping with Respect to a c-Distance on an Abstract Metric Space Endowed with a Graph
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Notes"
DOI: 10.1134/s0001434619050146
Abstract: In this paper, we prove the existence of fixed points for any mapping that is a Banach G-contraction with respect to a c-distance on a cone metric space endowed with a graph. read more here.
Keywords: space endowed; metric space; fixed points; endowed graph ... See more keywords
Caristi-Type Fixed Point Theorem over Száz Principle in Quasi-Metric Space with a Graph
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematics"
DOI: 10.1155/2019/8956083
Abstract: The aim of this paper is to generalize Caristi’s fixed point theorem in a K-complete quasi-metric space endowed with a reflexive digraph by using Száz maximum principle. An example is given to support our main… read more here.
Keywords: metric space; quasi metric; point theorem; fixed point ... See more keywords
Fixed Point Results of a New Family of Contractions in Metric Space Endowed with a Graph
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Mathematics"
DOI: 10.1155/2023/2534432
Abstract: In this note, a general class of contractive inequality, namely, admissible hybrid H − α − ϕ contraction, is proposed in metric space endowed with a graph, and new criteria for which the mapping is… read more here.
Keywords: fixed point; metric space; endowed graph; space endowed ... See more keywords