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Some Relationships between Filters*
Published online by Cambridge University Press: 20 November 2018
Extract
A filter is a set theoretical concept and as such, its structure is independent of any topology which can be put on the given space. However, an O-filter, whose counterpart in the theory of nets is the O-nets of Robertson and Franklin [2], is defined with respect to the topology on the given space. The purpose of this paper is to give necessary and sufficient conditions for every O-filter to be an ultrafilter and for every Cauchy filter to be an O-filter.
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- Research Article
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- Copyright © Canadian Mathematical Society 1967
Footnotes
An extract from the authors Masters thesis. The author gratefully acknowledges the help given by Dr. S.A. Naimpally.