On the embedding Menger n-groupoids in n-ary topological groups

Abstract

In [1] Regilhof proved that the binary cancellative ,abelian, locally compact semigroup when all of whose intern translations are open and continuous, is topologically embeddable in a locally compact binary topological group as an open subsemigroup. In this paper we prove a similar result for Menger n-groupoid X,   with the topology X  . And we concluded the continuity of the n-ary operation ( ) in all arguments in topology X  .