Principle of  equicontinuity for topological groups

A. R. Khan; S. H. Khan

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The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group $G$ that is not Dieudonné complete one can find a Dieudonné complete group $H$ such that the Dieudonné completion of $G \times H$ is not a topological group containing $G \times H$ as a subgroup. Using Korovin’s construction of $G_{δ}$ -dense orbits, we present some examples showing that some results on topological groups are not valid...