What kind of riemannian manifold is separable? [closed]

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It is true that a riemannian manifold equipped with the geodesic distance is a metric space $(M,d)$. What kind of riemannian manifold is separable, connected or others? By the way, is the sphere (equipped with the geodesic distance) separable?






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closed as off-topic by user99914, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister Sep 10 at 13:34


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  • What do you mean by others? It is true that any compact metric space is separable, therefore the sphere is seperable.
    – abcdef
    Sep 9 at 10:15














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It is true that a riemannian manifold equipped with the geodesic distance is a metric space $(M,d)$. What kind of riemannian manifold is separable, connected or others? By the way, is the sphere (equipped with the geodesic distance) separable?






real-analysis geometry







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migration rejected from mathoverflow.net Sep 10 at 13:34


This question came from our site for professional mathematicians. Votes, comments, and answers are locked due to the question being closed here, but it may be eligible for editing and reopening on the site where it originated.





closed as off-topic by user99914, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister Sep 10 at 13:34


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." – Community, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.












  • What do you mean by others? It is true that any compact metric space is separable, therefore the sphere is seperable.
    – abcdef
    Sep 9 at 10:15












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











It is true that a riemannian manifold equipped with the geodesic distance is a metric space $(M,d)$. What kind of riemannian manifold is separable, connected or others? By the way, is the sphere (equipped with the geodesic distance) separable?






real-analysis geometry







share|cite















It is true that a riemannian manifold equipped with the geodesic distance is a metric space $(M,d)$. What kind of riemannian manifold is separable, connected or others? By the way, is the sphere (equipped with the geodesic distance) separable?






real-analysis geometry




real-analysis geometry






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share|cite













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share|cite








edited Sep 9 at 10:04









Jendrik Stelzner

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7,69121137










asked Sep 6 at 16:21







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migration rejected from mathoverflow.net Sep 10 at 13:34


This question came from our site for professional mathematicians. Votes, comments, and answers are locked due to the question being closed here, but it may be eligible for editing and reopening on the site where it originated.





closed as off-topic by user99914, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister Sep 10 at 13:34


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." – Community, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.




migration rejected from mathoverflow.net Sep 10 at 13:34


This question came from our site for professional mathematicians. Votes, comments, and answers are locked due to the question being closed here, but it may be eligible for editing and reopening on the site where it originated.





closed as off-topic by user99914, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister Sep 10 at 13:34


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." – Community, Jendrik Stelzner, Xander Henderson, Delta-u, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.











  • What do you mean by others? It is true that any compact metric space is separable, therefore the sphere is seperable.
    – abcdef
    Sep 9 at 10:15
















  • What do you mean by others? It is true that any compact metric space is separable, therefore the sphere is seperable.
    – abcdef
    Sep 9 at 10:15















What do you mean by others? It is true that any compact metric space is separable, therefore the sphere is seperable.
– abcdef
Sep 9 at 10:15




What do you mean by others? It is true that any compact metric space is separable, therefore the sphere is seperable.
– abcdef
Sep 9 at 10:15















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