Give an example of subset $B$ of the real line $mathbb{R}$ so the subsets $A$, $Int(A)$, $overline{A}$, dont...
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What is an example of a subset $A$ of the real line $mathbb{R}$ (equipped with the standard metric topology), such that
the subsets $A$, $Int(A)$, $overline{A}$, $overline{Int(A)}$ and Int($overline{A}$) are pairwise different?
general-topology
asked Dec 3 at 11:35
Esteban Cambiasso
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put on hold as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 at 1:24
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What is an example of a subset $A$ of the real line $mathbb{R}$ (equipped with the standard metric topology), such that
the subsets $A$, $Int(A)$, $overline{A}$, $overline{Int(A)}$ and Int($overline{A}$) are pairwise different?
general-topology
asked Dec 3 at 11:35
Esteban Cambiasso
103
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 at 1:24
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." – amWhy, Brahadeesh, DRF, Lord_Farin, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.
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Welcome to mathSE. What have you tried? Where did you get stuck? Please add some information about your work done. As is the question will be closed.
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Dec 3 at 14:12
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up vote
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down vote
favorite
up vote
0
down vote
favorite
What is an example of a subset $A$ of the real line $mathbb{R}$ (equipped with the standard metric topology), such that
the subsets $A$, $Int(A)$, $overline{A}$, $overline{Int(A)}$ and Int($overline{A}$) are pairwise different?
general-topology
asked Dec 3 at 11:35
Esteban Cambiasso
103
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What is an example of a subset $A$ of the real line $mathbb{R}$ (equipped with the standard metric topology), such that
the subsets $A$, $Int(A)$, $overline{A}$, $overline{Int(A)}$ and Int($overline{A}$) are pairwise different?
general-topology
general-topology
asked Dec 3 at 11:35
Esteban Cambiasso
103
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 3 at 11:35
Esteban Cambiasso
103
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 21 hours ago
asked Dec 3 at 11:35
Esteban Cambiasso
103
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 3 at 11:35
Esteban Cambiasso
103
asked Dec 3 at 11:35
Esteban Cambiasso
103
103
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Esteban Cambiasso is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 at 1:24
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." – amWhy, Brahadeesh, DRF, Lord_Farin, KReiser
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 amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 at 1:24
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." – amWhy, Brahadeesh, DRF, Lord_Farin, KReiser
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Welcome to mathSE. What have you tried? Where did you get stuck? Please add some information about your work done. As is the question will be closed.
– DRF
Dec 3 at 14:12
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1
Welcome to mathSE. What have you tried? Where did you get stuck? Please add some information about your work done. As is the question will be closed.
– DRF
Dec 3 at 14:12
1
1
Welcome to mathSE. What have you tried? Where did you get stuck? Please add some information about your work done. As is the question will be closed.
– DRF
Dec 3 at 14:12
Welcome to mathSE. What have you tried? Where did you get stuck? Please add some information about your work done. As is the question will be closed.
– DRF
Dec 3 at 14:12
add a comment |
2 Answers
2
active
oldest
votes
up vote
3
down vote
accepted
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
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up vote
2
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Take $A=((0,1) cap mathbb{Q}) cup (2,3)$. The interior of A is $(2,3)$, the closure of A is $[0,1] cup [2,3]$, the closure of the interior of A is $[2,3]$, and the interior of the closure of A is $(0,1) cup (2,3)$.
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
add a comment |
up vote
3
down vote
accepted
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
answered Dec 3 at 11:39
Cameron Buie
84.6k771155
84.6k771155
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
add a comment |
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
ok, we got the same idea ahah (Typing latex with a phone is harder though)
– Antonio Alfieri
Dec 3 at 12:01
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
True! Hence my brevity. ;-)
– Cameron Buie
Dec 3 at 12:21
add a comment |
up vote
2
down vote
Take $A=((0,1) cap mathbb{Q}) cup (2,3)$. The interior of A is $(2,3)$, the closure of A is $[0,1] cup [2,3]$, the closure of the interior of A is $[2,3]$, and the interior of the closure of A is $(0,1) cup (2,3)$.
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
add a comment |
up vote
2
down vote
Take $A=((0,1) cap mathbb{Q}) cup (2,3)$. The interior of A is $(2,3)$, the closure of A is $[0,1] cup [2,3]$, the closure of the interior of A is $[2,3]$, and the interior of the closure of A is $(0,1) cup (2,3)$.
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
add a comment |
up vote
2
down vote
up vote
2
down vote
Take $A=((0,1) cap mathbb{Q}) cup (2,3)$. The interior of A is $(2,3)$, the closure of A is $[0,1] cup [2,3]$, the closure of the interior of A is $[2,3]$, and the interior of the closure of A is $(0,1) cup (2,3)$.
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
Take $A=((0,1) cap mathbb{Q}) cup (2,3)$. The interior of A is $(2,3)$, the closure of A is $[0,1] cup [2,3]$, the closure of the interior of A is $[2,3]$, and the interior of the closure of A is $(0,1) cup (2,3)$.
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
answered Dec 3 at 11:59
Antonio Alfieri
1,162412
1,162412
add a comment |
add a comment |
1
Welcome to mathSE. What have you tried? Where did you get stuck? Please add some information about your work done. As is the question will be closed.
– DRF
Dec 3 at 14:12