Ring-like Space Constructed from Group-like Space

The ring-like space introduced in1] is more extensive than the topological ring in view of the definition. But, in face, it has not been shown whether the ring-like space is really more extensive than the topological ring. In our study, we first investigate a method of constructing a ring-like space from a group-like space. Then, using this method, ws construct a ring-like space which is not a topological ring.