Is Openess and closedness are preserved under uniformly continuous map? [on hold]
up vote
-3
down vote
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Question: does uniformly continuous function maps open set to open set? and does uniformly continuous function maps closed set to closed set?
"I think they are false" but I couldn't able to find counter examples.plese help me..
uniform-continuity open-map closed-map
asked yesterday
Akash Patalwanshi
9011816
put on hold as off-topic by Brahadeesh, user21820, Holo, TheSimpliFire, amWhy yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, user21820, Holo, TheSimpliFire, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
-3
down vote
favorite
1
Question: does uniformly continuous function maps open set to open set? and does uniformly continuous function maps closed set to closed set?
"I think they are false" but I couldn't able to find counter examples.plese help me..
uniform-continuity open-map closed-map
asked yesterday
Akash Patalwanshi
9011816
put on hold as off-topic by Brahadeesh, user21820, Holo, TheSimpliFire, amWhy yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, user21820, Holo, TheSimpliFire, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
I don't know why negative votes? Isn't community is for those, who seeking help in Mathematics? Yes I am beiginner and doesn't able to find counter example. So what's wrong in it.
– Akash Patalwanshi
yesterday
add a comment |
up vote
-3
down vote
favorite
1
up vote
-3
down vote
favorite
1
1
Question: does uniformly continuous function maps open set to open set? and does uniformly continuous function maps closed set to closed set?
"I think they are false" but I couldn't able to find counter examples.plese help me..
uniform-continuity open-map closed-map
asked yesterday
Akash Patalwanshi
9011816
Question: does uniformly continuous function maps open set to open set? and does uniformly continuous function maps closed set to closed set?
"I think they are false" but I couldn't able to find counter examples.plese help me..
uniform-continuity open-map closed-map
uniform-continuity open-map closed-map
asked yesterday
Akash Patalwanshi
9011816
asked yesterday
Akash Patalwanshi
9011816
edited yesterday
asked yesterday
Akash Patalwanshi
9011816
asked yesterday
Akash Patalwanshi
9011816
asked yesterday
Akash Patalwanshi
9011816
9011816
put on hold as off-topic by Brahadeesh, user21820, Holo, TheSimpliFire, amWhy yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, user21820, Holo, TheSimpliFire, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Brahadeesh, user21820, Holo, TheSimpliFire, amWhy yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, user21820, Holo, TheSimpliFire, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
I don't know why negative votes? Isn't community is for those, who seeking help in Mathematics? Yes I am beiginner and doesn't able to find counter example. So what's wrong in it.
– Akash Patalwanshi
yesterday
add a comment |
I don't know why negative votes? Isn't community is for those, who seeking help in Mathematics? Yes I am beiginner and doesn't able to find counter example. So what's wrong in it.
– Akash Patalwanshi
yesterday
I don't know why negative votes? Isn't community is for those, who seeking help in Mathematics? Yes I am beiginner and doesn't able to find counter example. So what's wrong in it.
– Akash Patalwanshi
yesterday
I don't know why negative votes? Isn't community is for those, who seeking help in Mathematics? Yes I am beiginner and doesn't able to find counter example. So what's wrong in it.
– Akash Patalwanshi
yesterday
add a comment |
1 Answer
1
active
oldest
votes
up vote
4
down vote
accepted
Try $f(x)=sin x$. This has range $[-1,1]$. Also consider the image of
a set like ${2npi+1/n:ninBbb N}$.
answered yesterday
Lord Shark the Unknown
96.9k958128
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
|
show 1 more comment
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
Try $f(x)=sin x$. This has range $[-1,1]$. Also consider the image of
a set like ${2npi+1/n:ninBbb N}$.
answered yesterday
Lord Shark the Unknown
96.9k958128
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
|
show 1 more comment
up vote
4
down vote
accepted
Try $f(x)=sin x$. This has range $[-1,1]$. Also consider the image of
a set like ${2npi+1/n:ninBbb N}$.
answered yesterday
Lord Shark the Unknown
96.9k958128
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
|
show 1 more comment
up vote
4
down vote
accepted
up vote
4
down vote
accepted
Try $f(x)=sin x$. This has range $[-1,1]$. Also consider the image of
a set like ${2npi+1/n:ninBbb N}$.
answered yesterday
Lord Shark the Unknown
96.9k958128
Try $f(x)=sin x$. This has range $[-1,1]$. Also consider the image of
a set like ${2npi+1/n:ninBbb N}$.
answered yesterday
Lord Shark the Unknown
96.9k958128
answered yesterday
Lord Shark the Unknown
96.9k958128
answered yesterday
Lord Shark the Unknown
96.9k958128
answered yesterday
Lord Shark the Unknown
96.9k958128
96.9k958128
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
|
show 1 more comment
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
1
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Thanks sir, I think , the set ${2nπ+ 1/n: nin mathbb{N}}$ is closed as limit point $0$ is not in set and its image will be set $f(S)={sin(1/n): nin mathbb{N}}$ which is not closed as $sin(0)=0$ is not in $f(S)$ ? Am I correct? Further what about Openess?
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
Sir please elaborate
– Akash Patalwanshi
yesterday
1
1
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
@AkashPatalwanshi That's right. But although terse, my answer did address both openness and closedness. $ddotsmile$
– Lord Shark the Unknown
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
Oh got it sir...$ddotsmile$ is you want to say, $f(mathbb{R})=[-1,1]$ and hence f doesn't maps open set to an open set?
– Akash Patalwanshi
yesterday
1
1
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
@AkashPatalwanshi That's correct.
– Lord Shark the Unknown
yesterday
|
show 1 more comment
I don't know why negative votes? Isn't community is for those, who seeking help in Mathematics? Yes I am beiginner and doesn't able to find counter example. So what's wrong in it.
– Akash Patalwanshi
yesterday