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 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
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closed as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 '18 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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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 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
$endgroup$
closed as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 '18 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
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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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– DRF
Dec 3 '18 at 14:12
add a comment |
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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 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
$endgroup$
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 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
asked Dec 3 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
edited Dec 6 '18 at 8:54
Esteban Cambiasso
asked Dec 3 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
asked Dec 3 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
asked Dec 3 '18 at 11:35
Esteban CambiassoEsteban Cambiasso
103
103
closed as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 '18 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.
closed as off-topic by amWhy, Brahadeesh, DRF, Lord_Farin, KReiser Dec 4 '18 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
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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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– DRF
Dec 3 '18 at 14:12
add a comment |
1
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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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– DRF
Dec 3 '18 at 14:12
1
1
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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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– DRF
Dec 3 '18 at 14:12
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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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– DRF
Dec 3 '18 at 14:12
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2 Answers
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oldest
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Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
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ok, we got the same idea ahah (Typing latex with a phone is harder though)
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– Antonio Alfieri
Dec 3 '18 at 12:01
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True! Hence my brevity. ;-)
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– Cameron Buie
Dec 3 '18 at 12:21
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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 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
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add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
$endgroup$
$begingroup$
ok, we got the same idea ahah (Typing latex with a phone is harder though)
$endgroup$
– Antonio Alfieri
Dec 3 '18 at 12:01
$begingroup$
True! Hence my brevity. ;-)
$endgroup$
– Cameron Buie
Dec 3 '18 at 12:21
add a comment |
$begingroup$
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
$endgroup$
$begingroup$
ok, we got the same idea ahah (Typing latex with a phone is harder though)
$endgroup$
– Antonio Alfieri
Dec 3 '18 at 12:01
$begingroup$
True! Hence my brevity. ;-)
$endgroup$
– Cameron Buie
Dec 3 '18 at 12:21
add a comment |
$begingroup$
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
$endgroup$
Let $B=Bbb Qcap(1,2),$ and let $A=(0,1)cup B.$
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
answered Dec 3 '18 at 11:39
Cameron BuieCameron Buie
85.1k771155
85.1k771155
$begingroup$
ok, we got the same idea ahah (Typing latex with a phone is harder though)
$endgroup$
– Antonio Alfieri
Dec 3 '18 at 12:01
$begingroup$
True! Hence my brevity. ;-)
$endgroup$
– Cameron Buie
Dec 3 '18 at 12:21
add a comment |
$begingroup$
ok, we got the same idea ahah (Typing latex with a phone is harder though)
$endgroup$
– Antonio Alfieri
Dec 3 '18 at 12:01
$begingroup$
True! Hence my brevity. ;-)
$endgroup$
– Cameron Buie
Dec 3 '18 at 12:21
$begingroup$
ok, we got the same idea ahah (Typing latex with a phone is harder though)
$endgroup$
– Antonio Alfieri
Dec 3 '18 at 12:01
$begingroup$
ok, we got the same idea ahah (Typing latex with a phone is harder though)
$endgroup$
– Antonio Alfieri
Dec 3 '18 at 12:01
$begingroup$
True! Hence my brevity. ;-)
$endgroup$
– Cameron Buie
Dec 3 '18 at 12:21
$begingroup$
True! Hence my brevity. ;-)
$endgroup$
– Cameron Buie
Dec 3 '18 at 12:21
add a comment |
$begingroup$
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 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
$endgroup$
add a comment |
$begingroup$
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 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
$endgroup$
add a comment |
$begingroup$
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 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
$endgroup$
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 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
answered Dec 3 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
answered Dec 3 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
answered Dec 3 '18 at 11:59
Antonio AlfieriAntonio Alfieri
1,197412
1,197412
add a comment |
add a comment |
1
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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.
$endgroup$
– DRF
Dec 3 '18 at 14:12