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seen May 16 '11 at 4:24

May
16
awarded  Scholar
May
16
accepted Why is the base manifold of a Lie groupoid required to be second-countable?
May
16
awarded  Student
May
15
comment Why is the base manifold of a Lie groupoid required to be second-countable?
Another motivation for this question is: If one allows the manifold for the arrows to be non-Hausdorff (for good reasons), why not allow the base manifold to be non-second-countable?
May
15
comment Why is the base manifold of a Lie groupoid required to be second-countable?
Sorry, I should state this question more carefully. Of course, Zev Chonoles and Mariano Suarez-Alvarez are right: the usual definition of a manifold requires second-countability and Hausdorff and locally euclidean. My question should merely be: At which point in the theory of Lie groupoids does one really need that the base manifold is second-countable? When constructing a Lie groupoid from a foliation one actually has to be a bit careful at this point. If one takes uncountably many charts the base manifold of the Lie groupoid won't be second-countable.
May
15
asked Why is the base manifold of a Lie groupoid required to be second-countable?