### A completion construction for continuous dynamical systems

#### Abstract

In this work we use the theory of exterior spaces to construct a~$\check{C}_{0}^\mathbf{r}$-completion and a $\check{C}_{0}^\mathbf{l}$-completion of a dynamical

system. If $X$ is a~flow, we construct canonical maps $X\to

\check{C}_{0}^\mathbf{lr(X)$ and $X\to \check{C}_{0}^{\mathbf{l}}(X)$ and when these maps are

homeomorphisms we have the class of $\check{C}_{0}^{\mathbf{r}}$-complete and

$\check{C}_{0}^{\mathbf{l}}$-complete flows, respectively. In this study we find

out many relations between the topological properties of the

completions and the dynamical properties of a given flow. In the

case of a complete flow this gives interesting relations between

the topological properties (separability properties, compactness,

convergence of nets, etc.) and dynamical properties (periodic

points, omega limits, attractors, repulsors, etc.).

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