About M-bounded Topological Groups

Abstract

Although the theory of uniform spaces is independent, it is closely related to the theory of topological groups and there is a profound analogy between them. Therefore, research into the theory of topological groups using uniform structures is relevant. In this paper some important properties of the Mbounded topological group using uniform structures are investigated. In particular, it is established that under precompact continuous homomorphism, the M-bounded property is preserved both in the image and the preimage direction.