@article {
author = {Mohamadian, R. and Namdari, M. and Najafian, H. and Soltanpour, S.},
title = {A NOTE ON Cc(X) VIA A TOPOLOGICAL RING},
journal = {Journal of Algebraic Systems},
volume = {10},
number = {2},
pages = {323-334},
year = {2023},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2022.11467.1579},
abstract = {Let $C_c(X)$ (resp., $C_c^*(X)$) denote the functionallycountable subalgebra of $C(X)$ (resp., $C^*(X)$),consisting of all functions (resp., bounded functions) with countable image.$C_c(X)$ (resp., $C_c^*(X)$) as a topological ring via $m_c$-topology (resp., $m^*_c$-topology) and $u_c$-topology (resp., $u^*_c$-topology) is investigated and the equality of the latter two topologies is characterized. Topological spaces which are called $N$-spaces are introduced and studied.It is shown that the $m_c$-topology on $C_c(X)$ and its relative topology as a subspace of $C(X)$ (with $m$-topology) coincide if and only if $X$ is an $N$-space. We also show that $X$ is pseudocompact if and only if it is both a countably pseudocompact, and an $N$-space.},
keywords = {Functionally countable subalgebra,$m_c$-topology,$u_c$-topology,$N$-space},
url = {https://jas.shahroodut.ac.ir/article_2477.html},
eprint = {https://jas.shahroodut.ac.ir/article_2477_e924e7f0f47be03484e4067a481fe8a8.pdf}
}