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The topological structure of 𝒟–classes
Published online by Cambridge University Press: 17 April 2009
Abstract
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Let S be a compact, topological semigroup with identity. Suppose D, L and R are the D, L and R classes of some x ∈ S. Let (L, α., L/H), (R, β, R/H), (D, γ, D/H) and (D, δ, D/R) by the fibre spaces gotten where α, β γ an δ are the natural maps. It is shown that (D, γ, D/H) has topologically the same structure as the fibre space associated with (L, α, L/H) by R. Also if (L, α, L/H) is locally trivial (locally a cartesian product) then so is (D, δ, D/R) and if both (L, α, L/H) and (R, β, R/H) are locally trivial then so is (D, γ, D/H).
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 289 - 295
- Copyright
- Copyright © Australian Mathematical Society 1969
References
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