Robert A. McCoy
Fell topology and uniform topology on compacta on spaces of multifunctions
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 51, 127-136(1997)

MSC:

54C35 Function spaces, See also {46Exx, 58D15}

54B30 Categorical methods, See also {18B30}

Abstract: The set $2^{X\times Y}$ of closed subsets of
$X\times Y$ may be identified with the set of upper semicontinuous
multifunctions from $X$ into $2^{Y}$. This set contains the set
$C(X,Y)$ of continuous functions and the larger set $D(X,Y)$ of
densely continuous forms. In this paper, the Fell topology (a
hyperspace topology) and the uniform topology on compacta (a function
space topology) are both imposed on $2^{X\times Y}$ and compared.
Conditions are determined for the subspace $D(X,Y)$ to be dense in
$2^{X\times Y}$ under the Fell topology and to be closed in
$2^{X\times Y}$ under the uniform topology on compacta.
Keywords: Hyperspace, multifunction, Fell topology, uniform topology on compacta, densely continuous form