- #1

waternight

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## Homework Statement

A is a sequentially compact set, and B is a point ⃗v in Rn−A.

deﬁne the distance between A and B as dist( ⃗u0 , ⃗v), where you showed

that ⃗u0∈ A exists such that dist( ⃗u0 , ⃗v)≤dist(⃗u, ⃗v) for all ⃗u in A.

a) Use this example to state a deﬁnition of the distance between two sets in general,

giving the largest class of sets for which your deﬁnition works.

b) Prove that your deﬁnition is well deﬁned on the class of sets for which you say it

applies in a), and give counterexamples showing you can’t weaken the conditions in your

deﬁnition.

c) think of another deﬁnition of distance which applies to any two sets in Rn . Check that this second deﬁnition gives a reasonable answer for the distance between an open ball and its boundary. If you restrict this second deﬁnition to the class of sets considered in a) you should get the same answer as a).

## Homework Equations

## The Attempt at a Solution

I don't have any clue of writing the definition and the proof. What does the largest class of sets mean?