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I am reading here that in a Banach space, the sum of the closed unit ball with a closed bounded convex set might fail to be closed itself. It seems there is a counterexample if and only if the space fails to be reflexive.
This was a surprise, because I thought I had proved the sum is always cl...
In additive combinatorics, the sumset (also called the Minkowski sum) of two subsets
A
{\displaystyle A}
and
B
{\displaystyle B}
of an abelian group
G
{\displaystyle G}
(written additively) is defined to be the set of all sums of an element from
A
{\displaystyle A}
with an element from
B
{\displaystyle B}
. That is,
A
+
B
=
{...
In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B:
A
+
B
=
{
a
+
b
|
a
∈
A
,
b
∈
B
}
{\displaystyle A+B=\{\mathbf {a} +\mathbf {b} \,|\,\mathbf {a} \in A,\ \mathbf {b} \in B\}}
The Minkowski difference (also...
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