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International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 37-43
http://dx.doi.org/10.1155/S016117120000171X

Recapturing semigroup compactifications of a group from those of its closed normal subgroups

M. R. Miri1 and M. A. Pourabdollah2

1Department of Mathematics, University of Birjand, Birjand, Iran
2Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Received 8 January 1998; Revised 20 June 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We know that if S is a subsemigroup of a semitopological semigroup T, and 𝔉 stands for one of the spaces 𝒜𝒫,𝒲𝒜𝒫,𝒮𝒜𝒫,𝒟 or ℒ𝒞, and (ϵ,T𝔉) denotes the canonical 𝔉-compactification of T, where T has the property that 𝔉(S)=𝔉(T)|s, then (ϵ|s,ϵ(S)¯) is an 𝔉-compactification of S. In this paper, we try to show the converse of this problem when T is a locally compact group and S is a closed normal subgroup of T. In this way we construct various semigroup compactifications of T from the same type compactifications of S.