Pointfree topology version of image of real-valued continuous functions
Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2018-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | http://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdf |
| _version_ | 1819091867151630336 |
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| author | Abolghasem Karimi Feizabadi Ali Akbar Estaji Maryam Robat Sarpoushi |
| author_facet | Abolghasem Karimi Feizabadi Ali Akbar Estaji Maryam Robat Sarpoushi |
| author_sort | Abolghasem Karimi Feizabadi |
| collection | DOAJ |
| description | Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree version of $C_c(X).$The main aim of this paper is to present the pointfree version of image of real-valued continuous functions in $ {mathcal{R}} L$. In particular, we will introduce the pointfree version of the ring $C_c(X)$. We define a relation from $ {mathcal{R}} L$ into the power set of $mathbb R$, namely overlap. Fundamental properties of this relation are studied. The relation overlap is a pointfree version of the relation defined as $mathop{hbox{Im}} (f) subseteq S$ for every continuous function $f:Xrightarrowmathbb R$ and $ S subseteq mathbb R$. |
| first_indexed | 2024-12-21T22:46:32Z |
| format | Article |
| id | doaj.art-dc5effde5fac467e809a05179807db7c |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-21T22:46:32Z |
| publishDate | 2018-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-dc5effde5fac467e809a05179807db7c2022-12-21T18:47:41ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612018-07-0191597550745Pointfree topology version of image of real-valued continuous functionsAbolghasem Karimi Feizabadi0Ali Akbar Estaji1Maryam Robat Sarpoushi2Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Faculty of Mathematics and Computer Sciences,Hakim Sabzevari University, Sabzevar, Iran.Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree version of $C_c(X).$The main aim of this paper is to present the pointfree version of image of real-valued continuous functions in $ {mathcal{R}} L$. In particular, we will introduce the pointfree version of the ring $C_c(X)$. We define a relation from $ {mathcal{R}} L$ into the power set of $mathbb R$, namely overlap. Fundamental properties of this relation are studied. The relation overlap is a pointfree version of the relation defined as $mathop{hbox{Im}} (f) subseteq S$ for every continuous function $f:Xrightarrowmathbb R$ and $ S subseteq mathbb R$.http://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdfFramering of real-valued continuous functionscountable image$f$-ring |
| spellingShingle | Abolghasem Karimi Feizabadi Ali Akbar Estaji Maryam Robat Sarpoushi Pointfree topology version of image of real-valued continuous functions Categories and General Algebraic Structures with Applications Frame ring of real-valued continuous functions countable image $f$-ring |
| title | Pointfree topology version of image of real-valued continuous functions |
| title_full | Pointfree topology version of image of real-valued continuous functions |
| title_fullStr | Pointfree topology version of image of real-valued continuous functions |
| title_full_unstemmed | Pointfree topology version of image of real-valued continuous functions |
| title_short | Pointfree topology version of image of real-valued continuous functions |
| title_sort | pointfree topology version of image of real valued continuous functions |
| topic | Frame ring of real-valued continuous functions countable image $f$-ring |
| url | http://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdf |
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