A study of complete lattices of covering spaces

Abstract

Let C(X) denote the set of all covering spaces (X', x', p) of (X,x) where (X,x) are path connected,locally path connected and semilocally simply connected pointed topological spaces. In [1], it is shown that (C(X),≥) is a lattice with respect to the partial order relation ≥. Also (C(X),≥) is a modular, bounded and complete lattice when π(X,x) is abelian. In this paper, we will study some properties of the complete lattice (C(X), ≥).