Topological ring-groupoids and liftings


Ozcan A. F. , Icen I. , Gursoy M. H.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, cilt.30, ss.355-362, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 30
  • Basım Tarihi: 2006
  • Dergi Adı: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Sayfa Sayıları: ss.355-362

Özet

We prove that the set of homotopy classes of the paths in a topological ring is a topological ring object (called topological ring-groupoid). Let p : (X) over bar -> X be a covering map and let X be a topological ring. We define a category. UTRCov(X) of coverings of X in which both X and have universal coverings, and a category UTRGdCov(pi X-1) of coverings of topological ring-groupoid pi X-1, in which X and (R) over bar (0) = (X) over bar have universal coverings, and then prove the equivalence of these categories. We also prove that the topological ring structure of a topological ring-groupoid lifts to a universal topological covering groupoid.