一类新的关于脆点的双极软分离公理

IF 2 3区 数学 Q1 MATHEMATICS
Baravan A. Asaad, Sagvan Y. Musa
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引用次数: 1

摘要

摘要本研究的主要目的是定义一类新的双极软(BS)分离公理,称为BS T~i{\widetilde{\widetilde{T}}}_{i}-空间(i=0,1,2,3,4)\left(i=0、1、2、3、4)。这种类型是根据普通点定义的。我们证明了当i=1,2 i=1、2时,BS T~i{\widetilder{T}}_{i}-空间意味着BS T~i-1{\ widetilde{\Widetilder{T}}}_{i-1}-空间;然而,正如一个例子所表明的那样,相反的观点是不正确的。对于i=0,1,2,3,4 i=0,1,2,3,4,我们研究了每个BS T~i{\widetilder{\T}}_{i}-空间都是软T~i{\widettilder{T}}_{i-空间;并且我们建立了一个条件,在这个条件下,相反的情况成立。此外,我们指出,对于i=0,1,2,3 i=0,1,2,3,BS T~i{\widetilder{T}}_{i}-空间的BS子空间是BS T~i{\widetilter{\Widetilder{T}}_{i-空间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A novel class of bipolar soft separation axioms concerning crisp points
Abstract The main objective of this study is to define a new class of bipolar soft (BS) separation axioms known as BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space ( i = 0 , 1 , 2 , 3 , 4 ) \left(i=0,1,2,3,4) . This type is defined in terms of ordinary points. We prove that BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space implies BS T ˜ ˜ i − 1 {\widetilde{\widetilde{T}}}_{i-1} -space for i = 1 , 2 i=1,2 ; however, the opposite is incorrect, as demonstrated by an example. For i = 0 , 1 , 2 , 3 , 4 i=0,1,2,3,4 , we investigate that every BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space is soft T ˜ i {\widetilde{T}}_{i} -space; and we set up a condition in which the reverse is true. Moreover, we point out that a BS subspace of a BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space is a BS T ˜ ˜ i {\widetilde{\widetilde{T}}}_{i} -space for i = 0 , 1 , 2 , 3 i=0,1,2,3 .
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来源期刊
CiteScore
2.40
自引率
5.00%
发文量
37
审稿时长
35 weeks
期刊介绍: Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.
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