We wish to investigate some elementary problems concerning topological dynamics revolving around our proposed definition of escaping set. We also discuss the notion of escaping set in the induced dynamics of the hyperspace. Moreover, we extend the notion of limit set and escaping set for the general semigroup generated by continuous self maps.
Quotients of $\mathbb{N}^*$, $ω$-limit sets, and chain transitivity
The escaping set of the exponential
Escaping sets are not sigma-compact
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