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Net, Filters and Generalized Filters

S. Ramesh Kumar

Abstract


The concept of convergence is of fundamental importance in real and complex analysis. Most of the important concepts are defined or characterized in terms of a limit. In case of a metric space the limit concept is studied by using sequences. The inadequacy of sequential limits in topological spaces motivated the Mathematicians to introduce the limit concept in a most general way. Hence the new concept namely filters and nets were introduced.

In this paper, the concept of nets, filters and generalized filters are defined with examples and also discuss some theorems and studied their properties.


Keywords


Generalized Topology, Net, Filters and Generalized Filters.

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References


Baskaran R., Murugalingam M., Sivaraj D., “Generalized Nets in Generalized Topological Spaces”, Journal of Advanced Research in Pure Mathematics”, Vol. 2011, pp. 1-7. Online ISSN: 1943 - 2380.

Csaszar A., “Generalised Open Sets”, Acta. Math. Hungar. 75 (1 - 2) (1997) 65-87.

Palaniammal S, Murugalingam M, “ Generalized filters”, International Mathematical Forum, Vol.9,2014, no.36, 1751-1756.


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