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 / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/12624 |
| Date | 04 April 2013 |
| Creators | Toko, Wilson Bombe |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
Page generated in 0.0034 seconds