restricted 3- space can be a field?
0
$begingroup$
if the topological boundary set is non-empty; we can put a field structure.
for example 3-space is not a field but R^3-{Ox,Oy,Oz} is a field.
i want to know can this be a theorem?
set-theory
asked Jan 8 at 21:40
user117705user117705
1
$endgroup$
add a comment |
0
$begingroup$
if the topological boundary set is non-empty; we can put a field structure.
for example 3-space is not a field but R^3-{Ox,Oy,Oz} is a field.
i want to know can this be a theorem?
set-theory
asked Jan 8 at 21:40
user117705user117705
1
$endgroup$
1
$begingroup$
Every infinite set can be given a field structure. The result you are mentioning, that $mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense.
$endgroup$
– Wojowu
Jan 8 at 21:47
$begingroup$
math.stackexchange.com/questions/3065885/…
$endgroup$
– Asaf Karagila♦
Jan 8 at 22:08
add a comment |
0
0
0
$begingroup$
if the topological boundary set is non-empty; we can put a field structure.
for example 3-space is not a field but R^3-{Ox,Oy,Oz} is a field.
i want to know can this be a theorem?
set-theory
asked Jan 8 at 21:40
user117705user117705
1
$endgroup$
if the topological boundary set is non-empty; we can put a field structure.
for example 3-space is not a field but R^3-{Ox,Oy,Oz} is a field.
i want to know can this be a theorem?
set-theory
set-theory
asked Jan 8 at 21:40
user117705user117705
1
asked Jan 8 at 21:40
user117705user117705
1
asked Jan 8 at 21:40
user117705user117705
1
asked Jan 8 at 21:40
user117705user117705
1
asked Jan 8 at 21:40
user117705user117705
1
1
1
$begingroup$
Every infinite set can be given a field structure. The result you are mentioning, that $mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense.
$endgroup$
– Wojowu
Jan 8 at 21:47
$begingroup$
math.stackexchange.com/questions/3065885/…
$endgroup$
– Asaf Karagila♦
Jan 8 at 22:08
add a comment |
1
$begingroup$
Every infinite set can be given a field structure. The result you are mentioning, that $mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense.
$endgroup$
– Wojowu
Jan 8 at 21:47
$begingroup$
math.stackexchange.com/questions/3065885/…
$endgroup$
– Asaf Karagila♦
Jan 8 at 22:08
1
1
$begingroup$
Every infinite set can be given a field structure. The result you are mentioning, that $mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense.
$endgroup$
– Wojowu
Jan 8 at 21:47
$begingroup$
Every infinite set can be given a field structure. The result you are mentioning, that $mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense.
$endgroup$
– Wojowu
Jan 8 at 21:47
$begingroup$
math.stackexchange.com/questions/3065885/…
$endgroup$
– Asaf Karagila♦
Jan 8 at 22:08
$begingroup$
math.stackexchange.com/questions/3065885/…
$endgroup$
– Asaf Karagila♦
Jan 8 at 22:08
add a comment |
0
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1
$begingroup$
Every infinite set can be given a field structure. The result you are mentioning, that $mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense.
$endgroup$
– Wojowu
Jan 8 at 21:47
$begingroup$
math.stackexchange.com/questions/3065885/…
$endgroup$
– Asaf Karagila♦
Jan 8 at 22:08