\(\varepsilon \)-connectedness, finite approximations, shape theory and coarse graining in hyperspaces
As a starting point, this paper studies \(\varepsilon\)-connectedness. This concept was introduced by \textit{G. Cantor} [Math. Ann. 23, 453--488 (1884; JFM 16.0459.01)], and recently studied and applied by \textit{D. Snyder} [Physica D 173, No.~3--4, 131--136 (2002; Zbl 1007.54015)] and \textit{V. Robins}, \textit{J. D. Meiss} and \textit{E. Bradley} [Nonlinearity 11, No. 4, 913--922 (1998; Zbl 0957.54010)]. After establishing an important connection between \(\varepsilon\)-connectedness and shape theory, many related applications to computational topology and dynamics are stated. In this regard, the work of V. Robins and collaborators is noteworthy; references are provided.
scientific article; zbMATH DE number 5506281
scientific article