Comments on some mathematical contributions of Elon Lima.- The Spanier-Whitehead duality in new homotopy categories.- Stable Postnikov invariants and their duals.- Commuting vector fields on 2-manifolds.- On the local triviality of the restriction map for embeddings.- Commuting vector fields on S2.- Common singularities of commuting vector fields on 2-manifolds.- Commuting vector fields on S3.- Isometric immersions with semi-definite second quadratic forms.- Immersions of manifolds with non-negative sectional curvatures.- Orientability of smooth hypersurfaces and the Jordan-Brouwer separation theorem.- The Jordan-Brouwer separation theorem for smooth hypersurfaces.