I need some help/advice doing the following proof. Also, I'm in a beginning real analysis class and the section we're covering is on uniform continuity, so keep that in mind I guess.
Suppose
is uniformly continuous on each of the sets
and let
. Show that
need not be continuous on
. Show that, even if
is continuous on
,
need not be uniformly continuous on
.
I think it should suffice to show the result for
, since you could do a simple induction proof to show the result for up to
. Other than that though, I'm confused as to where I should even begin. Any help is greatly appreciated.