Local topological structure in the LUC compactification of a locally compact group
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Date
2007.
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Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007.
Abstract
In this thesis we first construct the LUC-Compactification of a topological group. We present GLUC with two different approaches, first as the set of multiplicative means on the space of LUC functions on G, and when G is locally compact, as a quotient space of the set of ultrafilters on G. Then local topological structure of GLUC is investigated and a neighborhood basis for elements of GLUC is characterized. Results on the injectivity property of multiplication on GLUC are obtained, and a special condition on G, under which injectivity property can be extended is also examined. Finally a subclass, the slowly oscillating functions, of LUC-functions is defined to decompose a special subspace of GLUC. Then the decomposition is extended to discrete cancellative semigroups.