Characterizations of Filter Convergent in Terms of Ideal

Year 2024, Volume: 37 Issue: 2, 912 - 922, 01.06.2024

Shyamapada Modak , Kulchhum Khatun Jiarul Hoque

https://doi.org/10.35378/gujs.967261

Cited By: 1

Abstract

In this paper, convergences of a filter and a net have been characterized through ideal on topological spaces. Furthermore, we characterized the local function in an ideal topological space in terms of convergence of filter. Using Zorn's Lemma, we have found a maximal element in the collection of all proper ideals on a nonempty set which is called maximal ideal. We provide a convenient characterization of maximal ideals. We also consider simple properties of the image of an ideal, a net and various local functions under a homeomorphism.

Keywords

Net, Filter, Ultrafilter, Ideal, Local Function

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