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Search: MSC category 54B20 ( Hyperspaces )

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1. CMB Online first

Chen, Chung-Chuan
Recurrence of cosine operator functions on groups
In this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.

Keywords:topologically multiple recurrence, recurrence, topological transitivity, hypercyclicity, cosine operator function
Categories:47A16, 54B20, 43A15

2. CMB 2011 (vol 54 pp. 607)

Camargo, Javier
Lightness of Induced Maps and Homeomorphisms
An example is given of a map $f$ defined between arcwise connected continua such that $C(f)$ is light and $2^{f}$ is not light, giving a negative answer to a question of Charatonik and Charatonik. Furthermore, given a positive integer $n$, we study when the lightness of the induced map $2^{f}$ or $C_n(f)$ implies that $f$ is a homeomorphism. Finally, we show a result in relation with the lightness of $C(C(f))$.

Keywords:light maps, induced maps, continua, hyperspaces
Categories:54B20, 54E40

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