Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4286
 Title: Dynamical Systems from Uniform Completions Authors: Garibay, F.Sanchis, M.Vera, R. Keywords: uniform completion; compactification; dynamical system; minimality; transitivity Issue Date: 2001 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Source: F. Garibay, M. Sanchis and R. Vera, "Dynamical Systems from Uniform Completions", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.2, pp. 47–57. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics32 (2001) suppl.2 Abstract: Let $\left(X,\mathcal{U}\right)$ be a compact uniform space, $\sum$the set of natural numbers or the integers, $\varphi\;:\; X\;\longrightarrow\; X$a continuous function or a homeomorphism. Given the dynamical system$\left(X,\varphi,\sum\right)$, an extension $\left(K,\widehat{\varphi,}\sum\right)$,can be constructed by letting K be the uniform completion of $\left(X,\mathcal{V}\right)$,where $\mathcal{V}$ is a totally bounded uniformity fi{}ner than$\mathcal{U}$. If D$_{f}$ means for the set $\left\{ x\:\epsilon\: X\:\mid\: f\::(X,\mathcal{U})\longrightarrow\mathbb{C}\; is\; discontinuous\; at\; x\right\} ,$ we prove that, if C(K) contains a dense subset E which contains nocharacteristic functions of singletons and such that, for each $f\epsilon E$, there exists a fi{}nite subset F of D$_{f}$ with $D_{f}\backslash F$discrete (in $\left(X,\mathcal{U}\right)$), then $\left(K,\widehat{\varphi,}\sum\right)$inherits the properties of minimality and topological transitivityfrom $\left(X,\varphi,\sum\right)$. Several open questions are posed. Type: Article URI: http://hdl.handle.net/10077/4286 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s2

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