Characterizations of Filter Convergent in Terms of Ideal

IF 1 Q3 MULTIDISCIPLINARY SCIENCES

gazi university journal of science Pub Date : 2023-09-24 DOI:10.35378/gujs.967261

Shyamapada MODAK, Kulchhum KHATUN, Jiarul HOQUE

引用次数: 0

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.

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滤波器在理想条件下收敛的特性

本文通过拓扑空间上的理想，刻画了滤波器和网络的收敛性。进一步，我们用滤波器的收敛性对理想拓扑空间中的局部函数进行了刻画。利用佐恩引理，在非空集合上的所有固有理想集合中找到了一个极大元素，称为极大理想。我们提供了极大理想的一个方便的表征。我们还考虑了理想象、网象和同胚下的各种局部函数的简单性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

gazi university journal of science MULTIDISCIPLINARY SCIENCES-

CiteScore

1.60

自引率

11.10%

发文量

期刊介绍： The scope of the “Gazi University Journal of Science” comprises such as original research on all aspects of basic science, engineering and technology. Original research results, scientific reviews and short communication notes in various fields of science and technology are considered for publication. The publication language of the journal is English. Manuscripts previously published in another journal are not accepted. Manuscripts with a suitable balance of practice and theory are preferred. A review article is expected to give in-depth information and satisfying evaluation of a specific scientific or technologic subject, supported with an extensive list of sources. Short communication notes prepared by researchers who would like to share the first outcomes of their on-going, original research work are welcome.