TY - JOUR ID - 2674 TI - On the essential $CP$-spaces JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Majidipour, Saham AU - Mohamadian, Rostam AU - Namdari, Mehrdad AU - Soltanpour, Somayeh AD - Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran AD - Department of Science, Ahvaz Faculty of Petroleum, Petroleum University of Technology, Ahvaz, Iran Y1 - 2022 PY - 2022 VL - 9 IS - 2 SP - 97 EP - 111 KW - Almost $CP$-point KW - $c$-basically disconnected KW - Essential almost $ CP$-point KW - Essential $CP$-space KW - $F_c$-space KW - Quasi $F_c$-space KW - Space of minimal prime ideals KW - Von Neumann local regular ring DO - 10.22034/as.2022.2674 N2 - Let $C_c(X)$ be the functionally countable subalgebra of $C(X)$. Essential $CP$-spaces are introduced and investigated algebraically and topologically. It is shown that if $X$ is a proper essential $CP$-space, then $mC_c(X)$ is compact if and only if $\{ \eta \}$ is a $G_\delta$, where $\eta$ is the only non $CP$-point of $X$ and $mC_c(X)$ is the space of minimal prime ideals of $C_c(X)$ which are not maximal. Quasi $F_c$-spaces, $c$-basically disconnect spaces, almost $CP$-spaces and almost essential $CP$-spaces are introduced and studied via essential $CP$-spaces. Finally, $C_c(X)$ as a $CSV$-ring where $X$ is an essential $CP$-space is investigated. UR - https://as.yazd.ac.ir/article_2674.html L1 - https://as.yazd.ac.ir/article_2674_c6eab8768fd228c71acb7067a118ac93.pdf ER -