Are there known examples of compact infinite dimensional manifolds?


The word "manifold" is important.



Are there examples of compact infinite dimensional manifolds?
The empty space is a manifold of any dimension.


No, seriously, let's assume that "manifold" means a Hausdorff space in which every point has an open neighborhood homeomorphic to an open subset of a topological vector space. If the manifold is compact and nonempty then the vector space must be locally compact. As far as I know, that makes it finite-dimensional.


