Our principle aim is to study an algebraic group properties topologically and specially essential
extension of topological groups. Among the results in paper are obtained. We show how you can find extension
and essential of topological groups by other given topological group.
Furthermore, new proposition (as we know) are given at the end of this work.
Key Words: Injective topological group, essential extension of topological group, topological group, direct
sum.
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