(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# I am not sure - a manifold is locally connected and has countable basis?

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