Prove that spheres in $2$ and $3$ dimensions are not homeomorphic.Homework question on whether two quotient spaces are homeomorphicWhich of the following pairs of sets are homeomorphic of the following?Showing that two Banach spaces are homeomorphic when their dimensions are equal.$X$ and $Y$ are homeomorphic. Show that also their one-point compactifications are homeomorphic.Find homeomorphic and non-homeomorphic pairs among the spaces $A, B$ and $C$.Is the following pairs of set are homeomorphic?Are $mathbbQ$ and $mathbbZ$ homeomorphic?Different p-adic topologies on $mathbbQ $ are homeomorphicIf $n>m$, then the spheres $S^n$ and $S^m$ are not homeomorphic?Show two topological spaces are homeomorphic
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Prove that spheres in $2$ and $3$ dimensions are not homeomorphic.
Homework question on whether two quotient spaces are homeomorphicWhich of the following pairs of sets are homeomorphic of the following?Showing that two Banach spaces are homeomorphic when their dimensions are equal.$X$ and $Y$ are homeomorphic. Show that also their one-point compactifications are homeomorphic.Find homeomorphic and non-homeomorphic pairs among the spaces $A, B$ and $C$.Is the following pairs of set are homeomorphic?Are $mathbbQ$ and $mathbbZ$ homeomorphic?Different p-adic topologies on $mathbbQ $ are homeomorphicIf $n>m$, then the spheres $S^n$ and $S^m$ are not homeomorphic?Show two topological spaces are homeomorphic
$begingroup$
The spaces $S^1$ and $S^2$, with their topologies inherited from $mathbb R^2$ and $mathbb R^3$, respectively, are not homeomorphic. Here $S^1$ and $S^2$ are spheres in $2$ and $3$ dimension.
general-topology
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
$endgroup$
add a comment |
$begingroup$
The spaces $S^1$ and $S^2$, with their topologies inherited from $mathbb R^2$ and $mathbb R^3$, respectively, are not homeomorphic. Here $S^1$ and $S^2$ are spheres in $2$ and $3$ dimension.
general-topology
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
$endgroup$
add a comment |
$begingroup$
The spaces $S^1$ and $S^2$, with their topologies inherited from $mathbb R^2$ and $mathbb R^3$, respectively, are not homeomorphic. Here $S^1$ and $S^2$ are spheres in $2$ and $3$ dimension.
general-topology
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
$endgroup$
The spaces $S^1$ and $S^2$, with their topologies inherited from $mathbb R^2$ and $mathbb R^3$, respectively, are not homeomorphic. Here $S^1$ and $S^2$ are spheres in $2$ and $3$ dimension.
general-topology
general-topology
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
edited Mar 14 at 8:42
Asaf Karagila♦
306k33438769
306k33438769
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
asked Mar 14 at 6:31
Mittal GMittal G
1,379516
1,379516
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
If you remove two points from $S^1$ it becomes disconnected. But if you remove two points from $S^2$ it does not become disconnected.
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
$endgroup$
add a comment |
$begingroup$
Remove two points from $S^1$ and it's not connected. Remove two points from $S^2$ and it remains connected.
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
If you remove two points from $S^1$ it becomes disconnected. But if you remove two points from $S^2$ it does not become disconnected.
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
$endgroup$
add a comment |
$begingroup$
If you remove two points from $S^1$ it becomes disconnected. But if you remove two points from $S^2$ it does not become disconnected.
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
$endgroup$
add a comment |
$begingroup$
If you remove two points from $S^1$ it becomes disconnected. But if you remove two points from $S^2$ it does not become disconnected.
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
$endgroup$
If you remove two points from $S^1$ it becomes disconnected. But if you remove two points from $S^2$ it does not become disconnected.
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
answered Mar 14 at 6:33
Kavi Rama MurthyKavi Rama Murthy
68.6k53169
68.6k53169
add a comment |
add a comment |
$begingroup$
Remove two points from $S^1$ and it's not connected. Remove two points from $S^2$ and it remains connected.
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
$endgroup$
add a comment |
$begingroup$
Remove two points from $S^1$ and it's not connected. Remove two points from $S^2$ and it remains connected.
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
$endgroup$
add a comment |
$begingroup$
Remove two points from $S^1$ and it's not connected. Remove two points from $S^2$ and it remains connected.
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
$endgroup$
Remove two points from $S^1$ and it's not connected. Remove two points from $S^2$ and it remains connected.
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
answered Mar 14 at 6:33
Robert ShoreRobert Shore
3,225323
3,225323
add a comment |
add a comment |
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