Ideals in Stone-Cech compactifications
Date
2013-04-04
Authors
Toko, Wilson Bombe
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Abstract
Let S be an in nite discrete semigroup and S the Stone- Cech compacti
cation of S. The operation of S naturally extends to S and makes S
a compact right topological semigroup with S contained in the topological
center of S. The aim of this thesis is to present the following new
results.
1. If S embeddable in a group, then S contains 22jSj pairwise incomparable
semiprincipal closed two-sided ideals.
2. Let S be an in nite cancellative semigroup of cardinality and
U(S) the set of uniform ultra lters on S. If > !, then there is a
closed left ideal decomposition of U(S) such that the corresponding
quotient space is homeomorphic to U( ). If = !, then for
any connected compact metric space X, there is a closed left ideal
decomposition of U(S) with the quotient space homeomorphic to
X.
Description
A thesis submitted in ful llment of the
requirements for the degree of Doctor of Philosophy
in Mathematics
School of Mathematics
University of the Witwatersrand
Johannesburg
October, 2012