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Minima and maxima. We fix a positive integer n.
 

Summary: Minima and maxima.
We fix a positive integer n.
Whenever a Rn
and 0 < r < we let
U(a, r) = {x Rn
: |x - a| < r} and B(a, r) = {x Rn
: |x - a| r};
the first of these sets is called the open ball with center a and radius r and
the second is called the closed ball with center a and radius r.
We now fix a subset A of Rn
.
We let
int A = {x Rn
: U(a, r) A for some r with 0 < r < };
cl A = {x Rn
: A U(a, r) = whenever 0 < r < };
bdry A = cl A cl (Rn
A);
these sets are called the interior, closure and boundary of A, respectively.
We now suppose that

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics