A STUDY OF COVERING SPACES THROUGH LATTICES - Rana, Dr. Pravanjan Kumar; Hossain, Sarmad; Mandal, Bhaskar (IJRDO -JOURNAL OF MATHEMATICS, 2023)
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 this paper we show that: (i)(C(X),≥) is a lattice and (C^r(X),≥) is a subllatice of (C(X),≥) without assuming π(X,x) is abelian,where C^r(X) is the set of all regular covering spaces of (X,x). (ii)(C(X),≥) is a modular,bounded and complete lattice when π(X,x) is abelian.