TY - JOUR
ID - 50745
TI - Pointfree topology version of image of real-valued continuous functions
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Karimi Feizabadi, Abolghasem
AU - Estaji, Ali Akbar
AU - Robat Sarpoushi, Maryam
AD - Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran.
AD - Faculty of Mathematics and Computer Sciences,
Hakim Sabzevari University, Sabzevar, Iran.
AD - Faculty of Mathematics and Computer Sciences,Hakim Sabzevari University, Sabzevar, Iran.
Y1 - 2018
PY - 2018
VL - 9
IS - 1
SP - 59
EP - 75
KW - frame
KW - ring of real-valued continuous functions
KW - countable image
KW - $f$-ring
DO - 10.29252/cgasa.9.1.59
N2 - 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$.
UR - https://cgasa.sbu.ac.ir/article_50745.html
L1 - https://cgasa.sbu.ac.ir/article_50745_d90d55e08316779860740922b0388294.pdf
ER -