  We define submersions f between manifolds M and N modelled on locally convex
spaces. If the range N is finite-dimensional or a Banach manifold, then these
coincide with the naive notion of a submersion. We study pre-images of
submanifolds under submersions and pre-images under mappings whose
differentials have dense image. An infinite-dimensional version of the constant
rank theorem is provided. We also construct manifold structures on homogeneous
spaces G/H of infinite-dimensional Lie groups. Some fundamentals of immersions
between infinite-dimensional manifolds are developed as well.
