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Metric Mean Dimension via Preimage Structures
Journal of Statistical PhysicsLet \((X, d)\) be a compact metric space and \(f : X\to X\) be a continuous map. \textit{M. Hurley} [Ergodic Theory Dyn. Syst. 15, No. 3, 557--568 (1995; Zbl 0833.54021)] introduced the topological preimage entropy of \(f\) as follows \[ h_m(f)=\lim_{\varepsilon \rightarrow 0} h_m(f,\varepsilon ) =\underset{n\rightarrow \infty }{\lim \sup }\frac{1}{n ...
Chunlin Liu, Fagner B. Rodrigues
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Metric dimensions of metric spaces over integers
Quaestiones Mathematicae, 2019We consider metric spaces over the ring of integers. For any generating set S of ℤ, it is shown that the metric dimension of the metric space X = X(ℤ, S) is not greater than 2 max S.
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Metric dimension and strong metric dimension in annihilator-ideal graphs
Applicable Algebra in Engineering, Communication and ComputingR. Shahriyari +3 more
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Metric Dimension and Secure Metric Dimension of Some Graphs
Applied Mathematics & Information Sciencesopenaire +1 more source