A STUDY OF COVERING SPACES THROUGH LATTICES

  • Dr. Pravanjan Kumar Rana Associate Professor and Head, Department of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara, Kolkata
  • Sarmad Hossain Ph.D., Research Scholar, Department of Mathematics, Rama krishna Mission Vivekananda Centenary College, Rahara, Kolkata
  • Bhaskar Mandal Ph.D., Research Scholar, Department of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara, Kolkata
DOI: https://doi.org/10.53555/m.v9i1.5338
Keywords: fundamental group, covering space, universal covering,regular covering,covering homomorphism,lattice.

Abstract

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. 

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References

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Published
2023-01-10
How to Cite
Rana, D. P. K., Hossain, S., & Mandal, B. (2023). A STUDY OF COVERING SPACES THROUGH LATTICES. IJRDO -JOURNAL OF MATHEMATICS, 9(1), 19-23. https://doi.org/10.53555/m.v9i1.5338
Issue
Vol. 9 No. 1 (2023): IJRDO - JOURNAL OF MATHEMATICS (ISSN: 2455-9210)
Section
Articles

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