𝓜𝓝-convergence and lim-inf𝓜-convergence in partially ordered sets-Reference-Cited by-同舟云学术

𝓜𝓝-convergence and lim-inf𝓜-convergence in partially ordered sets

Published:2018-01-01 Issue:1 Volume:16 Page:1077-1090
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Sun Tao¹,Li Qingguo²,Fan Nianbai³

Affiliation:

1. Department of Math , Hunan University of Arts and Science , Changde , Hunan 415000 , China

2. College of Mathematics and Econometrics , Hunan University , Changsha , Hunan 410082 , China

3. College of Computer Science and Electronic Engineering , Hunan University , Changsha , Hunan 410082 , China

Abstract

Abstract In this paper, we first introduce the notion of 𝓜𝓝-convergence in posets as an unified form of O-convergence and O 2-convergence. Then, by studying the fundamental properties of 𝓜𝓝-topology which is determined by 𝓜𝓝-convergence according to the standard topological approach, an equivalent characterization to the 𝓜𝓝-convergence being topological is established. Finally, the lim-inf𝓜-convergence in posets is further investigated, and a sufficient and necessary condition for lim-inf𝓜-convergence to be topological is obtained.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2018-0090/pdf

Reference20 articles.

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4. Zhao B., Zhao D.S., Lim-inf-convergence in partially ordered sets, J. Math. Anal. Appl., 2005, 309, 701-708.

5. Wang K.Y., Zhao B., Some further results on order-convergence in posets, Topol. Appl., 2013, 160, 82-86.

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