Re: Distance between a closed and a compact set is positive.

In article <1146159716.333637.184940@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
alencar1980 <alencar1980@xxxxxxxxxx> wrote:
Dear all,

I'm stuck in the following problem.

Let V be a normed spaca. If C is a closed subset of V and K a compact
subset of V such that C \intersection K = \emptyset then there exist a
r>0 such that
||c-k||>= r for all c \in C and k \in K.

The slick way uses the fact that a continuous real-valued function on
a compact set has a minimum value.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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