Types of Filter and Ultra-filter with applications
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Abstract
The aim of this paper is to study the notion classes of filter and ultra-filter with application. In section one, types of filter have been introduced
Principle, non-principle, maximal and prime filter with some basic properties are studied and we establish a proof of some important properties. If be a filter on the set , and let , either:There is some , s.t or : there is some , is a filter on M. Frechet filter is also introduced in this paper. In section, two of this paper is the major contribution; we introduced two important application with new proof of ultra-filter in additive measure theory and Boolean algebra. There are one to one corresponding of ultra-filters on and finitely additive measure and Boolean algebra defined on
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