Extended topology: Filters and convergence I

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1965 Germany English Publisher:Springer Science and Business Media LLCJournal:Mathematische Annalen, volume 158, pages 57-68 (issn: 0025-5831, eissn: 1432-1807,

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Authors: THAMPURAN, D.V.;

doi: 10.1007/bf01370396

Extended topology: Filters and convergence I

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Abstract

The above-mentioned results show some of the advantages of using extended filters. It has already been shown that the family of all proper extended filters forms a complete lattice. Many of the results obtained by using Cartan's filters can be obtained by using proper extended filters; it is not necessary to impose the condition that they should be closed with respect to finite intersections. And for most purposes it is sufficient if extended filters have the pair-wise intersection property; for instance limits are unique under this condition.

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Germany

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Keywords

510.mathematics, topology, Article

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