Question

Is the Minkowski sum of a compact set and a closed set necessarily closed?

score 5.8k · Answer 1 · 2011-11-10 23:56:03

5.8k

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Is the Minkowski sum of a compact set and a closed set necessarily closed?

Published on 10 Nov 2011 - 23:56

score 3.6k · Answer 2 · 2012-08-28 02:50:25

3.6k

Views

If $A$ and $B$ are compact, then so is $A+B$.

Published on 28 Aug 2012 - 2:50

score 62 · Answer 3 · 2020-09-25 02:01:11

62

Views

A finite Fibonacci sum

Published on 25 Sep 2020 - 2:01

score 56 · Answer 4 · 2020-10-30 14:50:52

56

Views

Dimension of sumset

Published on 30 Oct 2020 - 14:50

score 36 · Answer 5 · 2021-01-06 12:08:40

36

Views

Banach spaces, $\lVert\cdot\rVert_X$ and $\lVert\cdot\rVert_{X+X}$ are equivalent.

Published on 06 Jan 2021 - 12:08

score 74 · Answer 6 · 2021-02-10 12:55:42

74

Views

Minkowski sum of disks in 3D

Published on 10 Feb 2021 - 12:55

score 338 · Answer 7 · 2021-03-14 16:27:19

338

Views

Minkowski sum of the intersection of a closed and an open set with a compact set

Published on 14 Mar 2021 - 16:27

score 151 · Answer 8 · 2021-04-08 16:12:33

151

Views

For any $n-1$ non-zero elements of $\mathbb Z/n\mathbb Z$, we can make zero using $+,-$ if and only if $n$ is prime

Published on 08 Apr 2021 - 16:12

score 58 · Answer 9 · 2021-04-20 15:07:22

58

Views

Which sets of $n-1$ non-multiples of $n$ can't make a multiple of $n$ using $+,-$?

Published on 20 Apr 2021 - 15:07

score 62 · Answer 10 · 2021-08-24 15:28:15

62

Views

Sumsets : optimality of two basic inequalities

Published on 24 Aug 2021 - 15:28

score 81 · Answer 11 · 2021-09-23 13:51:15

Instead of "sum-free" sets, consider sets where $S\subset S+S$. This is trivially satisfied when $0 \in S$. Is there a subset of $S$ with sum $0$?

score 89 · Answer 12 · 2021-10-23 03:53:37

89

Views

How many subsets $S$ of integer interval $[0,n]$ such that $k \not \in S+S$?

Published on 23 Oct 2021 - 3:53

score 63 · Answer 13 · 2021-10-27 22:36:05

63

Views

Generating restricted finite additive $2$-bases from doubly-eager bit-strings

Published on 27 Oct 2021 - 22:36

score 39 · Answer 14 · 2022-01-31 01:08:40

39

Views

Is this true for a sumset?

Published on 31 Jan 2022 - 1:08

score 52 · Answer 15 · 2022-07-05 13:19:37

52

Views

Name for a shape consisting of the union of all spheres of a given radius centered at all points in a triangular (or tetrahedral) region?

Published on 05 Jul 2022 - 13:19

List Question

Is the Minkowski sum of a compact set and a closed set necessarily closed?

If $A$ and $B$ are compact, then so is $A+B$.

A finite Fibonacci sum

Dimension of sumset

Banach spaces, $\lVert\cdot\rVert_X$ and $\lVert\cdot\rVert_{X+X}$ are equivalent.

Minkowski sum of disks in 3D

Minkowski sum of the intersection of a closed and an open set with a compact set

For any $n-1$ non-zero elements of $\mathbb Z/n\mathbb Z$, we can make zero using $+,-$ if and only if $n$ is prime

Which sets of $n-1$ non-multiples of $n$ can't make a multiple of $n$ using $+,-$?

Sumsets : optimality of two basic inequalities

Instead of "sum-free" sets, consider sets where $S\subset S+S$. This is trivially satisfied when $0 \in S$. Is there a subset of $S$ with sum $0$?

How many subsets $S$ of integer interval $[0,n]$ such that $k \not \in S+S$?

Generating restricted finite additive $2$-bases from doubly-eager bit-strings

Is this true for a sumset?

Name for a shape consisting of the union of all spheres of a given radius centered at all points in a triangular (or tetrahedral) region?

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