make the given text more coherent
Some spheres are not hyperspheres: if S is a sphere in E where m < n and the space has n dimensions, then S is not a hypersphere. Any n-sphere in a proper flat is not a hypersphere.
Some spheres are not hyperspheres: if S is a sphere in E where m < n and the space has n dimensions, then S is not a hypersphere. Similarly, any n-sphere in a proper flat is not a hypersphere.