General Mathematics, Vol. 10,nr. 1-2, 2002
Abstract:
The aim of this paper is the study of a fixed point property
for
pairs of classes of topological spaces defined as follows:
for a class of sets $\varphi $ and a set $X$ we shall denote by
\[
\mathcal{C} (X)= \{C\in \mathcal{C} : C\subset X\} \ \mbox{and} \
\mathcal{C}^{*}(X) = \{C\in \mathcal{C} (X): C\neq \varnothing \}.
\]
We say that a map $T:X \to Y$ has $\mathcal{C} $ (resp.
$\mathcal{C}^{*}$) values if for each $x\in X$, $T(x)\in
\mathcal{C} (X)$ (resp. $T(x)\in \mathcal{C}^{*}(X)$).
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