Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
entropy; merotopic space; self-mapping; diameter function
entropy; merotopic space; self-mapping; diameter function
Summary:
For mappings $f\,:\, S\rightarrow S$, where $S$ is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the $\delta $-entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the $\delta $-entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of $S^N$, which is closely connected with the $\delta $-entropy of $f\,:\, S\rightarrow S$.
References:
[AKM65] Adler K.A, Kohnheim A., McAndrew M.: Topological entropy. Trans. Amer. Math. Soc. 114 (1965), 309-319. MR 0175106
[B71] Bowen R.: Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc. 153 (1971), 401-414. MR 0274707 | Zbl 0212.29201
[B73] Bowen R.: Topological entropy for noncompact sets. Trans. Amer. Math. Soc. 184 (1973), 125-156. MR 0338317
[F62] Frolík Z.: A characterization of topologically complete spaces in the sense of E. Čech in terms of convergence of functions. Czechoslovak Math. J. 13 (88) (1962), 148-151. MR 0155290
[H74] Herrlich H.: Topological structures. Proc. Sympos. in honour of J. de Groot, pp. 59-122, Math. Centre Tracts, no. 52, Math. Centrum, Amsterdam, 1974. MR 0358706 | Zbl 0589.54018
[H82] Herrlich H.: Categorical topology 1971-1981. Proc. Fifth Prague Topological Sympos. 1981, pp. 279-383; Heldermann, Berlin, 1982. MR 0698425 | Zbl 0502.54001
[K76] Katětov M.: Spaces defined by giving a family of centered systems (in Russian). Uspehi Mat. Nauk 31 (1976), no. 5 (191), 95-107 Russian Math. Surveys 31, (1976), 111-123. MR 0448278
[K90] Katětov M.: On entropy-like functionals and codes for metrized probability spaces I. Comment. Math. Univ. Carolinae 31 (1990), 49-66. MR 1056171
[K92a] Katětov M.: On entropy-like functionals and codes for metrized probability spaces II. Comment. Math. Univ. Carolinae 33 (1992), 79-95. MR 1173750
[K92b] Katětov M.: Entropy-like functionals: conceptual background and some results. Comment. Math. Univ. Carolinae 33 (1992), 645-660. MR 1240186
Search
Partner of
