Geodesic
The omega limit sets of subsets in a metric space
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 87-96

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In this paper, we discuss the properties of limit sets of subsets and attractors in a compact metric space. It is shown that the $\omega $-limit set $\omega (Y)$ of $Y$ is the limit point of the sequence $\lbrace (\mathop {\mathrm Cl}Y)\cdot [i,\infty )\rbrace _{i=1}^{\infty }$ in $2^X$ and also a quasi-attractor is the limit point of attractors with respect to the Hausdorff metric. It is shown that if a component of an attractor is not an attractor, then it must be a real quasi-attractor.
Classification : 34C35, 37B25, 37B30, 37C10, 54H20
Keywords: limit set of a set; attractor; quasi-attractor; hyperspace 
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     title = {The omega limit sets of subsets in a metric space},
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Ding, Changming. The omega limit sets of subsets in a metric space. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 87-96. http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a4/