- #1
mahmoud2011
- 88
- 0
I am not sure -- a manifold is locally connected and has countable basis?
There is an Exercise in a book as following :
Given a Manifold M , if N is a sub-manifold , an V is open set then V [itex]\cap[/itex] N is a countable collection of connected open sets .
I am asking why he put this exercise for only the case of sub-manifold , Is n't this an immediate consequence of the fact that a manifold is locally connected and has countable basis ?
I am not sure from what I say ?? I think there can't be exercise as easy as I think , I think I am wrong .
Thanks
There is an Exercise in a book as following :
Given a Manifold M , if N is a sub-manifold , an V is open set then V [itex]\cap[/itex] N is a countable collection of connected open sets .
I am asking why he put this exercise for only the case of sub-manifold , Is n't this an immediate consequence of the fact that a manifold is locally connected and has countable basis ?
I am not sure from what I say ?? I think there can't be exercise as easy as I think , I think I am wrong .
Thanks