Abstract
In this paper the concept of convergence defined by filters is used and applied in the study of semigroups. Special emphasis is placed on compact convergence semigroups and their properties.
Highlights
Let / be the set of all subsets of a non-empty set S which contains {x}
F(X) and P(X) which satisfy the following conditions: i) x, forallx6X; ii) if ’-xand ’
If the convergence structure is fixed for a specific discussion, as in reference to a general convergence space
Summary
Let / be the set of all subsets of a non-empty set S which contains {x}. is an ultra.filter called the principle ulrafilfer In [1], Kent’s approach to convergence was to set up a mapping q from F(X), the set of all filters on a set X, to P(X), the power ,c* of X. Let (X, q) and (Y, p) be convergence spaces and f" X Y. If X is a compact convergence space and T a closed subset of X, T is compact. If X is a compact space, and 2) is a descending family of non-empty closed subsets of X, N:D }. If X is a Hausdorff convergence space and T a compact subset of X,
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