## Tsukuba Journal of Mathematics

### Induced mappings on hyperspaces

Hiroshi Hosokawa

#### Abstract

Let $f:X\rightarrow Y$ be a mapping between continua. Then $f$ induces two mappings $C(f):C(X)\rightarrow C(Y)$ and $2^{f}:2^{X}\rightarrow 2^{Y}$ in the natural way. In this paper, we shall study about the following question: Dose the correspondences $f\rightarrow C(f)$ and $f\rightarrow 2^{f}$ preserve or reverse what classes of mappings? When $Y$ is locally connected, many classes of mappings are preserved by these correspondences. We shall consider the classes of monotone, open, OM, confluent, quasi-monotone and weakly monotone mappings.

#### Article information

Source
Tsukuba J. Math., Volume 21, Number 1 (1997), 239-250.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163175

Digital Object Identifier
doi:10.21099/tkbjm/1496163175

Mathematical Reviews number (MathSciNet)
MR1467235

Zentralblatt MATH identifier
0948.54016

#### Citation

Hosokawa, Hiroshi. Induced mappings on hyperspaces. Tsukuba J. Math. 21 (1997), no. 1, 239--250. doi:10.21099/tkbjm/1496163175. https://projecteuclid.org/euclid.tkbjm/1496163175