Problem 3\ Let

K

and

A

be nonempty disjoint compact sets. We define the distance,

d

, between

K

and

A

to be\

d=inf{|x-y|:xinK,yinA}.

\ (a) Show if

K

and

A

are disjoint then

d>0

.\ (b) Show if

K

and

A

are just disjoint and nonempty closed sets then it is possible to have

d=0

.

Let K and A be nonempty disjoint compact sets. We define the distance, d, between K and A to be d=inf{xy:xK,yA}. (a) Show if K and A are disjoint then d>0. (b) Show if K and A are just disjoint and nonempty closed sets then it is possible to have d=0