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Some Relationships between Filters*

Published online by Cambridge University Press:  20 November 2018

Ivan Baggs
Ivan Baggs*
Affiliation:
University of Alberta, Edmonton
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Extract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 257 - 260
Copyright
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.

References

1. Baggs, I., Nets and Filters in Topology. Masters thesis, University of Alberta, Edmonton, 1966.Google Scholar
2. Robertson, L. C. and Franklin, S. P., O-sequences and O-nets. Amer. Math. Monthly, 72 (1966), 506-510.Google Scholar
3. Sieber, J. L. and Pervin, W. J.. Completeness in quasiuniform spaces. Math. Ann., 158 (1966), 79-81.Google Scholar