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Acta Mathematica Vietnamica

, Volume 43, Issue 2, pp 257–273 | Cite as

Unique Path Lifting from Homotopy Point of View

  • Mehdi Tajik
  • Behrooz Mashayekhy
  • Ali Pakdaman
Article
  • 65 Downloads

Abstract

The paper introduces some notions extending the unique path lifting property from a homotopy viewpoint and studies their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting property and find all possible relationships between them. Moreover, we supplement the full relationships of these new notions in the presence of fibrations. Second, we deduce some results in the category of fibrations with these notions instead of unique path lifting such as the existence of products and coproducts. Also, we give a brief comparison of these new categories to some categories of the other generalizations of covering maps. Finally, we present two subgroups of the fundamental group related to the fibrations with these notions and compare them to the subgroups of the fundamental group related to covering and generalized covering maps.

Keywords

Homotopically lifting Unique path lifting Fibration Fundamental group Covering map 

Mathematics Subject Classification (2010)

55P05 57M10 57M05 

Notes

Acknowledgements

The authors thank the referee for his/her careful reading and useful suggestions. This research was supported by a grant from Ferdowsi University of Mashhad-Graduate Studies (No. 31685).

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of Pure MathematicsFerdowsi University of MashhadMashhadIran
  2. 2.Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic StructuresFerdowsi University of MashhadMashhadIran
  3. 3.Department of Mathematics, Faculty of SciencesGolestan UniversityGorganIran

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