Are there known examples of compact infinite dimensional manifolds?
The word "manifold" is important.
Are there known examples of compact infinite dimensional manifolds? The word "manifold" is important. 

closed as unclear what you're asking by BS., Andrey Rekalo, Carlo Beenakker, Ricardo Andrade, David White Oct 25 '13 at 12:44Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question. 


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 finitedimensional. 


Yes. Compact Hilbert cube manifolds, for instance. 

