Geodesic
Some Relationships between Filters*
Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 257-260

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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. 
Baggs, Ivan. Some Relationships between Filters*. Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 257-260. doi: 10.4153/CMB-1967-025-4
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[1] 1. Baggs, I., Nets and Filters in Topology. Masters thesis, University of Alberta, Edmonton, 1966. Google Scholar

[2] 2. Robertson, L. C. and Franklin, S. P., O-sequences and O-nets. Amer. Math. Monthly, 72 (1966), 506-510. Google Scholar

[3] 3. Sieber, J. L. and Pervin, W. J.. Completeness in quasiuniform spaces. Math. Ann., 158 (1966), 79-81. Google Scholar

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