# open sets in metric spacesWatch

#1
Hey does anyone know how to answer this question. Decide weather A={(x1, x2, x3) E R^3 : x1^2 + x2^2 E (-infinity, 1] and x3=1} is an open, closed, both, or neither open or closed subset in X=R^3 with the usual exclude an metric d2
0
4 years ago
#2
(Original post by lmassey)
Hey does anyone know how to answer this question. Decide weather A={(x1, x2, x3) E R^3 : x1^2 + x2^2 E (-infinity, 1] and x3=1} is an open, closed, both, or neither open or closed subset in X=R^3 with the usual exclude an metric d2
Don't understand the phrase in bold. Is this the usual euclidean metric?

Might help to draw the set, then it should be clear.
0
#3
Yh i sorry I did mean euclidean
0
4 years ago
#4
Try to picture it. Does it look open or closed?
0
#5
I think it's closed just not sure how to prove it .
0
4 years ago
#6
(Original post by lmassey)
I think it's closed just not sure how to prove it .

What does it mean for a set to be closed? How do you think you would start to prove it?
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Cardiff Metropolitan University
Sat, 27 Apr '19
• University of East Anglia
Could you inspire the next generation? Find out more about becoming a Primary teacher with UEA… Postgraduate
Sat, 27 Apr '19
• Anglia Ruskin University
Health, Education, Medicine and Social Care; Arts, Humanities and Social Sciences; Business and Law; Science and Engineering Undergraduate
Sat, 27 Apr '19

### Poll

Join the discussion

#### Have you registered to vote?

Yes! (551)
37.84%
No - but I will (114)
7.83%
No - I don't want to (102)
7.01%
No - I can't vote (<18, not in UK, etc) (689)
47.32%