Title: Specification properties on uniform spaces,
Abstract: In the following text we introduce specification property (stroboscopical
property) for dynamical systems on uniform space. We focus on two classes of
dynamical systems: generalized shifts and dynamical systems with Alexandroff
compactification of a discrete space as phase space. We prove that for a
discrete finite topological space $X$ with at least two elements, a nonempty
set $\Gamma$ and a self--map $\varphi:\Gamma\to\Gamma$ the generalized shift
dynamical system $(X^\Gamma,\sigma_\varphi)$: \begin{itemize} \item has
(almost) weak specification property if and only if $\varphi:\Gamma\to\Gamma$
does not have any periodic point,
\item has (uniform) stroboscopical property if and only if
$\varphi:\Gamma\to\Gamma$
is one-to-one. \end{itemize}