Fdtxjr

How could a scammer know the apps on my phone / iTunes account?

how to write formula in word in latex

How to deal with taxi scam when on vacation?

Identifying the interval from A♭ to D♯

Official degrees of earth’s rotation per day

PTIJ: Who should I vote for? (21st Knesset Edition)

Did Ender ever learn that he killed Stilson and/or Bonzo?

How to write cleanly even if my character uses expletive language?

Why do Australian milk farmers need to protest supermarkets' milk price?

Why doesn't the EU now just force the UK to choose between referendum and no-deal?

Can a druid choose the size of its wild shape beast?

Is a party consisting of only a bard, a cleric, and a warlock functional long-term?

If curse and magic is two sides of the same coin, why the former is forbidden?

Professor being mistaken for a grad student

Do I need life insurance if I can cover my own funeral costs?

How to explain that I do not want to visit a country due to personal safety concern?

Interplanetary conflict, some disease destroys the ability to understand or appreciate music

Python if-else code style for reduced code for rounding floats

Why one should not leave fingerprints on bulbs and plugs?

My Graph Theory Students

Brexit - No Deal Rejection

What is the significance behind "40 days" that often appears in the Bible?

Should we release the security issues we found in our product as CVE or we can just update those on weekly release notes?

Have researchers managed to "reverse time"? If so, what does that mean for physics?

proof compactness of sets

2 questions regarding compactness and closedCharacterization of compactness in weak* topologyContinuous one-to-one mapping of a compact spaceCharacterizing $sigma$-compactness via closed setsMetric space and compactnessa problem about compactness and sequential compactness in metric spaceProof that boundedness of continuous Real Valued functions implies CompactnessShow compactnessChecking the compactness of setsCompactness in the compact complement topology

0

$begingroup$

Let $$K ⊂ R^m$$ and $$L ⊂ R^n$$ be compact subsets.

Show:

a) The set $$ K × L: = (x, y): x ∈ K, y ∈ L ⊂ R^m+n$$ is also compact.

I have to show that this is bounded and closed.
But how do I do that?

compactness

share|cite|improve this question

edited Mar 11 at 23:50

breakshooter

asked Mar 11 at 21:14

breakshooterbreakshooter

11

New contributor

breakshooter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Please see math.meta.stackexchange.com/questions/5020/…
  $endgroup$
  – Lord Shark the Unknown
  Mar 11 at 21:15
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Bounded should not be a problem in either case. Have you tried proving that either $Ktimes L$ or $K+L$ is closed? What would the structure of such a proof look like?
  $endgroup$
  – Greg Martin
  Mar 11 at 22:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't know, can you help me?
  $endgroup$
  – breakshooter
  Mar 11 at 23:51
  

  
  
  
  

add a comment | 

0

$begingroup$

Let $$K ⊂ R^m$$ and $$L ⊂ R^n$$ be compact subsets.

Show:

a) The set $$ K × L: = (x, y): x ∈ K, y ∈ L ⊂ R^m+n$$ is also compact.

I have to show that this is bounded and closed.
But how do I do that?

compactness

share|cite|improve this question

edited Mar 11 at 23:50

breakshooter

asked Mar 11 at 21:14

breakshooterbreakshooter

11

New contributor

breakshooter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Please see math.meta.stackexchange.com/questions/5020/…
  $endgroup$
  – Lord Shark the Unknown
  Mar 11 at 21:15
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Bounded should not be a problem in either case. Have you tried proving that either $Ktimes L$ or $K+L$ is closed? What would the structure of such a proof look like?
  $endgroup$
  – Greg Martin
  Mar 11 at 22:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't know, can you help me?
  $endgroup$
  – breakshooter
  Mar 11 at 23:51
  

  
  
  
  

add a comment | 

$begingroup$

Let $$K ⊂ R^m$$ and $$L ⊂ R^n$$ be compact subsets.

Show:

a) The set $$ K × L: = (x, y): x ∈ K, y ∈ L ⊂ R^m+n$$ is also compact.

I have to show that this is bounded and closed.
But how do I do that?

compactness

share|cite|improve this question

edited Mar 11 at 23:50

breakshooter

asked Mar 11 at 21:14

breakshooterbreakshooter

11

New contributor

breakshooter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 11 at 23:50

breakshooter

asked Mar 11 at 21:14

breakshooterbreakshooter

11

New contributor

breakshooter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 11 at 23:50

breakshooter

asked Mar 11 at 21:14

breakshooterbreakshooter

11

New contributor

breakshooter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 11 at 21:14

breakshooterbreakshooter

11

New contributor

breakshooter is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 11 at 21:14

breakshooterbreakshooter

11