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Search: MSC category 54E40 ( Special maps on metric spaces )

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1. 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, hyperspacesCategories:54B20, 54E40

2. CMB 2010 (vol 53 pp. 719)

Stasyuk, I.; Tymchatyn, E. D.
 A Continuous Extension Operator for Convex Metrics We consider the problem of simultaneous extension of continuous convex metrics defined on subcontinua of a Peano continuum. We prove that there is an extension operator for convex metrics that is continuous with respect to the uniform topology. Categories:54E35, 54C20, 54E40