User dave lewis - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T08:34:01Z http://mathoverflow.net/feeds/user/15128 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65068/why-is-the-base-manifold-of-a-lie-groupoid-required-to-be-second-countable Why is the base manifold of a Lie groupoid required to be second-countable? Dave Lewis 2011-05-15T20:38:58Z 2011-05-15T22:38:24Z <p>I wonder why one requires that the base manifold of a Lie groupoid is second-countable? </p> http://mathoverflow.net/questions/65068/why-is-the-base-manifold-of-a-lie-groupoid-required-to-be-second-countable Comment by Dave Lewis Dave Lewis 2011-05-15T20:57:10Z 2011-05-15T20:57:10Z 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? http://mathoverflow.net/questions/65068/why-is-the-base-manifold-of-a-lie-groupoid-required-to-be-second-countable Comment by Dave Lewis Dave Lewis 2011-05-15T20:57:07Z 2011-05-15T20:57:07Z 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.