What are the topological qualities that define a plane? [on hold]
In terms of topological properties, is there any conclusive "list" of properties (such as compactness or connectedness)that can be said to conclusively define a sphere? Similarly, does such a list of properties exist for defining a plane of $n-1$ dimensions in $n$ dimensions?
general-topology geometric-topology
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
put on hold as unclear what you're asking by Moishe Cohen, Saad, mrtaurho, Lord_Farin, ancientmathematician Jan 5 at 14:39
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
In terms of topological properties, is there any conclusive "list" of properties (such as compactness or connectedness)that can be said to conclusively define a sphere? Similarly, does such a list of properties exist for defining a plane of $n-1$ dimensions in $n$ dimensions?
general-topology geometric-topology
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
put on hold as unclear what you're asking by Moishe Cohen, Saad, mrtaurho, Lord_Farin, ancientmathematician Jan 5 at 14:39
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
See, for instance, this link for a rather famous attempt at classifying spheres by a certain topological property.
– Arthur
Jan 4 at 14:58
4
There are lots of characterizations of planes. It’s better if you have a specific problem in mind.
– Charlie Frohman
Jan 4 at 15:20
1
Are you looking for a list of properties such that a space $X$ obeys them iff $X$ is homeomorphic to $mathbb{R}^2$ ?
– Henno Brandsma
Jan 4 at 16:52
You also seem to confuse planes and spheres.
– Moishe Cohen
Jan 4 at 22:12
add a comment |
In terms of topological properties, is there any conclusive "list" of properties (such as compactness or connectedness)that can be said to conclusively define a sphere? Similarly, does such a list of properties exist for defining a plane of $n-1$ dimensions in $n$ dimensions?
general-topology geometric-topology
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
In terms of topological properties, is there any conclusive "list" of properties (such as compactness or connectedness)that can be said to conclusively define a sphere? Similarly, does such a list of properties exist for defining a plane of $n-1$ dimensions in $n$ dimensions?
general-topology geometric-topology
general-topology geometric-topology
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
asked Jan 4 at 14:47
Aryaman GuptaAryaman Gupta
336
336
put on hold as unclear what you're asking by Moishe Cohen, Saad, mrtaurho, Lord_Farin, ancientmathematician Jan 5 at 14:39
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as unclear what you're asking by Moishe Cohen, Saad, mrtaurho, Lord_Farin, ancientmathematician Jan 5 at 14:39
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
See, for instance, this link for a rather famous attempt at classifying spheres by a certain topological property.
– Arthur
Jan 4 at 14:58
4
There are lots of characterizations of planes. It’s better if you have a specific problem in mind.
– Charlie Frohman
Jan 4 at 15:20
1
Are you looking for a list of properties such that a space $X$ obeys them iff $X$ is homeomorphic to $mathbb{R}^2$ ?
– Henno Brandsma
Jan 4 at 16:52
You also seem to confuse planes and spheres.
– Moishe Cohen
Jan 4 at 22:12
add a comment |
2
See, for instance, this link for a rather famous attempt at classifying spheres by a certain topological property.
– Arthur
Jan 4 at 14:58
4
There are lots of characterizations of planes. It’s better if you have a specific problem in mind.
– Charlie Frohman
Jan 4 at 15:20
1
Are you looking for a list of properties such that a space $X$ obeys them iff $X$ is homeomorphic to $mathbb{R}^2$ ?
– Henno Brandsma
Jan 4 at 16:52
You also seem to confuse planes and spheres.
– Moishe Cohen
Jan 4 at 22:12
2
2
See, for instance, this link for a rather famous attempt at classifying spheres by a certain topological property.
– Arthur
Jan 4 at 14:58
See, for instance, this link for a rather famous attempt at classifying spheres by a certain topological property.
– Arthur
Jan 4 at 14:58
4
4
There are lots of characterizations of planes. It’s better if you have a specific problem in mind.
– Charlie Frohman
Jan 4 at 15:20
There are lots of characterizations of planes. It’s better if you have a specific problem in mind.
– Charlie Frohman
Jan 4 at 15:20
1
1
Are you looking for a list of properties such that a space $X$ obeys them iff $X$ is homeomorphic to $mathbb{R}^2$ ?
– Henno Brandsma
Jan 4 at 16:52
Are you looking for a list of properties such that a space $X$ obeys them iff $X$ is homeomorphic to $mathbb{R}^2$ ?
– Henno Brandsma
Jan 4 at 16:52
You also seem to confuse planes and spheres.
– Moishe Cohen
Jan 4 at 22:12
You also seem to confuse planes and spheres.
– Moishe Cohen
Jan 4 at 22:12
add a comment |
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2
See, for instance, this link for a rather famous attempt at classifying spheres by a certain topological property.
– Arthur
Jan 4 at 14:58
4
There are lots of characterizations of planes. It’s better if you have a specific problem in mind.
– Charlie Frohman
Jan 4 at 15:20
1
Are you looking for a list of properties such that a space $X$ obeys them iff $X$ is homeomorphic to $mathbb{R}^2$ ?
– Henno Brandsma
Jan 4 at 16:52
You also seem to confuse planes and spheres.
– Moishe Cohen
Jan 4 at 22:12