In algebraic structures the substructures have a simple and clear definition. For instance, subgroup, subring, subalgebra, subfield, vector subspace, and so on. Manifolds are supposed to be but curved versions of such, so to say, straight or linear algebraic structures. However, when it comes to submanifolds and other more or less nice subsets, we have quite some complications. For instance, as subset can be an immersion, without being a submanifold. Or it can be a submanifold, without being an imbedding. Could one perhaps given another definition of manifold in which such complications do not arise, and we are back to the simplicity and clarity of algebra ?