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 $(\tilde{X},\tilde{x},p)$ 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)$(C(X),\geq)$ is a lattice and $(C^r(X),\geq)$ is a subllatice of $(C(X),\geq)$ without assuming $\pi(X,x)$ is abelian,where $C^r(X)$ is the set of all regular covering spaces of $(X,x)$.\\(ii)$(C(X),\geq)$ is a modular,bounded and complete lattice when $\pi(X,x)$ is abelian.