TY - JOUR
ID - 2477
TI - A NOTE ON Cc(X) VIA A TOPOLOGICAL RING
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Mohamadian, R.
AU - Namdari, M.
AU - Najafian, H.
AU - Soltanpour, S.
AD - Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box
6135783151, Ahvaz, Iran.
AD - Department of Science, Petroleum University of Technology, P.O. Box 6318714317,
Ahvaz, Iran.
Y1 - 2023
PY - 2023
VL - 10
IS - 2
SP - 323
EP - 334
KW - Functionally countable subalgebra
KW - $m_c$-topology
KW - $u_c$-topology
KW - $N$-space
DO - 10.22044/jas.2022.11467.1579
N2 - 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.
UR - https://jas.shahroodut.ac.ir/article_2477.html
L1 - https://jas.shahroodut.ac.ir/article_2477_e924e7f0f47be03484e4067a481fe8a8.pdf
ER -