T0-Closure Operators and Pre-Orders
B. Venkateswarlu, U. Maddana Swamy · Lobachevskii Journal of Mathematics · 2018
It is well known that the lattice of closed subsets of any topological space is isomorphic to that of a T 0 -topological space. This result is extended to lattices of closed subsets with respect to arbitrary closure operator on a set. Also, we establish a one-to-one correspondence between closure operators which are both algebraic and topological on a given set X and pre-orders on X and prove that this correspondence induces a one-to-one correspondence between topological algebraic T 0 -closure operators on X and partial orders on X .