Convergence of subsets
The notion of convergence in the "Hausdorff metric" is used
implicitly throughout this paper. However, since the concept will not be
used in its full generality, the following notation is introduced for the
special case of interest here.
Let
,
, be a sequence of subsets of
, and let
. The notation
means that
(1)
,
(2)
, and
(3)
neighborhood
of
,
, such that
.
Recall
that, if
is compact for every
, then so is
. If, in
addition, each
is nonempty, then so is
.
Copyright (c) 1998 by Richard
McGehee, all rights reserved.
Last modified: July 31, 1998.