bio | website | |
---|---|---|
location | ||
age | ||
visits | member for | 4 years, 3 months |
seen | May 16 '11 at 4:24 | |
stats | profile views | 13 |
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? |