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二元拓扑空间的分离性质

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2023-04-03 DOI:10.1155/2023/4384483

Xiaoli Qiang, S. Omidi, P. Sathishmohan, Lavanya Kakimallaiah, K. Rajalakshmi

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This new idea gives the notion of generalized binary (\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>0</mn>\n </mrow>\n </msub>\n </math>\n , \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n </math>\n , \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </math>\n , \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n </math>\n , and \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n </math>\n spaces) and binary generalized semi (\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>0</mn>\n </mrow>\n </msub>\n </math>\n , \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n </math>\n , \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </math>\n , \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n </math>\n , and \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M10\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n </math>\n spaces) using generalized binary open sets and binary generalized semi open sets to investigate their properties. We also provide adequate examples to assist and understand abstract concepts. In the similar manner, we begin researching the b-sg-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M11\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>0</mn>\n </mrow>\n </msub>\n </math>\n , b-sg-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M12\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n </math>\n , b-sg-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M13\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </math>\n , b-sg-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M14\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n </math>\n , and b-sg-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M15\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n </math>\n spaces in binary topological spaces. The study on the axioms is done over binary-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M16\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>0</mn>\n </mrow>\n </msub>\n </math>\n , binary-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M17\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n </math>\n , binary-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M18\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </math>\n , binary-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M19\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n </math>\n , and binary-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M20\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n </math>\n spaces, motivated to do the analysis of the spaces gb(b-gs)-\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M21\">\n <msub>\n <mrow>\n <mi>T</mi>\n </mrow>\n ","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Separation Properties of Binary Topological Spaces\",\"authors\":\"Xiaoli Qiang, S. 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We also provide adequate examples to assist and understand abstract concepts. In the similar manner, we begin researching the b-sg-\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M11\\\">\\n <msub>\\n <mrow>\\n <mi>T</mi>\\n </mrow>\\n <mrow>\\n <mn>0</mn>\\n </mrow>\\n </msub>\\n </math>\\n , b-sg-\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M12\\\">\\n <msub>\\n <mrow>\\n <mi>T</mi>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n </math>\\n , b-sg-\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M13\\\">\\n <msub>\\n <mrow>\\n <mi>T</mi>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n </math>\\n , b-sg-\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M14\\\">\\n <msub>\\n <mrow>\\n <mi>T</mi>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msub>\\n </math>\\n , and b-sg-\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M15\\\">\\n <msub>\\n <mrow>\\n <mi>T</mi>\\n </mrow>\\n <mrow>\\n <mn>4</mn>\\n </mrow>\\n </msub>\\n </math>\\n spaces in binary topological spaces. 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引用次数: 0

摘要

在本研究中，我们引入了一些新的二元拓扑空间的分离公理。这个新思想给出了广义二进制的概念（T 0，T1.t2，t3，和T4空间）和二元广义半空间（T 0，T1.t2，t3，和T4空间），利用广义二元开集和二元广义半开集来研究它们的性质。我们还提供了足够的例子来帮助和理解抽象概念。以类似的方式我们开始研究b-sg-T0，b-sg-T1，b-sg-T2，b-sg-T3，以及二元拓扑空间中的b-sg-T4空间。对公理的研究是在二进制-T0上进行的，二进制-T1，二进制-T2，二进制-T3，和二进制-T4空间，对空间gb（b-gs）-T进行分析的动机

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The Separation Properties of Binary Topological Spaces

In the present study, we introduce some new separation axioms for binary topological spaces. This new idea gives the notion of generalized binary (

T_{0}

T_{1}

T_{2}

T_{3}

, and

T_{4}

spaces) and binary generalized semi (

T_{0}

T_{1}

T_{2}

T_{3}

, and

T_{4}

spaces) using generalized binary open sets and binary generalized semi open sets to investigate their properties. We also provide adequate examples to assist and understand abstract concepts. In the similar manner, we begin researching the b-sg-

T_{0}

, b-sg-

T_{1}

, b-sg-

T_{2}

, b-sg-

T_{3}

, and b-sg-

T_{4}

spaces in binary topological spaces. The study on the axioms is done over binary-

T_{0}

, binary-

T_{1}

, binary-

T_{2}

, binary-

T_{3}

, and binary-

T_{4}

spaces, motivated to do the analysis of the spaces gb(b-gs)-

T

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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.