For a topological space 
, let 
denote the family of nonempty compact
sets in 
.
The Vietoris topology on 
has as a topological basis
the sets
 |
where 
,
..., 
are open sets in 
(Vietoris 1922; Illanes and Nadler 1999, Chap. 1). If
is a compact metric space, the Hausdorff
metric induces the Vietoris topology on 
.
