J-spaces and C-normal spaces: An algebraic perspective

Abstract

In this article, algebraic characterisations of J-spaces and C-normal spaces are exhibited. The concept of a Z-connected ideal in C(X) is presented and characterised using certain connected subsets of X. We define the class of JC-spaces and characterise its members via Z-connected ideals. Two more classes of ideals in C(X), namely the coz-free and F-free ideals, are instituted. These types of ideals are used to establish conditions under which a given space is a strong J-space. We introduce the notion of a J-lattice and show that the lattice, CL(X), of closed subsets of X is a J-lattice if and only if X is a J-space. A pointfree topology exposition of J-lattices is also presented, with more attention to complete Boolean algebras.