@article {
author = {Karimi Feizabadi, Abolghasem and Estaji, Ali Akbar and Robat Sarpoushi, Maryam},
title = {Pointfree topology version of image of real-valued continuous functions},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {59-75},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.59},
abstract = {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 $f:X\rightarrow\mathbb R$ and $ S \subseteq \mathbb R$.},
keywords = {frame,ring of real-valued continuous functions,countable image,$f$-ring},
url = {https://cgasa.sbu.ac.ir/article_50745.html},
eprint = {https://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdf}
}