Let

$X$ be a paracompact topological space,

$Y$ a hyperconvex metric space and

$F:X\to Y$ a multifunction with sub-admissible values. A subset

$B\subset Y$ is called sub-admissible if

$coC\subset B$ for each finite

$C\subset B$, where

$coC$ denotes the intersection of all closed balls in

$Y$ containing

$C$. It is proved that if

$F$ is quasi-lsc (i.e., for each

$x\in X$ and

$\epsilon >0$ there is a point

$y\in F\left(x\right)$ and a neighbourhood

$U\left(x\right)$ of

$x$ such that for each

$t\in U\left(x\right)$,

$F\left(t\right)\cap B(y,\epsilon )\ne \varnothing )$, then

$F$ admits a continuous selection. Two fixed-point theorems are deduced. Remark: It would be interesting to locate the generalized convexity used in the paper under review in the framework of Bielawski’s simplicial convexity, cf.

*R. Bielawski* [J. Math. Anal. Appl, 127, 155–171 (1987;

Zbl 0638.52002)].