Recapturing semigroup compactifications of a group from those of its closed normal subgroups
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 s...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117120000171X |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |