Characterizations of Filter Convergent in Terms of Ideal

Authors : Shyamapada Modak, Kulchhum Khatun, Jiarul Hoque

Pages : 912-922

Doi:10.35378/gujs.967261

View : 86 | Download : 154

Publication Date : 2024-06-01

Article Type : Research Paper

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