Ultrafilter semigroups

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dc.contributor.author Shuungula, Onesmus
dc.date.accessioned 2011-06-21T13:06:51Z
dc.date.available 2011-06-21T13:06:51Z
dc.date.issued 2011-06-21
dc.identifier.uri http://hdl.handle.net/10539/10146
dc.description.abstract (1) Given a local left topological group X with a distinguished element 0, denote by Ult(X) the subsemigroup of X consisting of all nonprinci- pal ultra lters on X converging to 0. Any two countable nondiscrete zero-dimensional local left topological groups X and Y with count- able bases are locally isomorphic and, consequently, the subsemigroups Ult(X) X and Ult(Y ) Y are isomorphic. However, not every two homeomorphic zero-dimensional local left topological groups are locally isomorphic. In the rst result of this thesis it is shown that for any two homeomorphic direct sums X and Y , the semigroups Ult(X) and Ult(Y ) are isomorphic. (2) Let S be a discrete semigroup, let S be the Stone- Cech compacti- cation of S, and let T be a closed subsemigroup of S. The second and main result of this thesis consists of characterizing ultra lters from the smallest ideal K(T) of T and from its closure c` K(T), and show- ing that for a large class of closed subsemigroups T of S, c` K(T) is not an ideal. This class includes the subsemigroups 0+ Rd and H ( L Z2). v en_US
dc.language.iso en en_US
dc.title Ultrafilter semigroups en_US
dc.type Thesis en_US


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