On the essential CP-spaces

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.

کلیدواژه ها:

Almost CP-point ، c-basically disconnected ، Essential almost CP-point ، Essential CP-space ، F_c-space ، Quasi F_c-space ، Space of minimal prime ideals ، Von Neumann local regular ring