TY - JOUR
AU - Rana, Dr. Pravanjan Kumar
AU - Hossain, Sarmad
AU - Mandal, Bhaskar
PY - 2023/01/10
Y2 - 2024/04/24
TI - A STUDY OF COVERING SPACES THROUGH LATTICES
JF - IJRDO -JOURNAL OF MATHEMATICS
JA - m
VL - 9
IS - 1
SE - Articles
DO - 10.53555/m.v9i1.5338
UR - https://ijrdo.org/index.php/m/article/view/5338
SP - 19-23
AB - 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.
ER -