Author/Authors :
FATIH OZCAN، A نويسنده Inonu University, Science and Art Faculty Department of Mathematics, Malatya, Turkey , , ICEN، I نويسنده Inonu University, Science and Art Faculty Department of Mathematics, Malatya, Turkey , , HABIL GURSOY، M نويسنده Inonu University, Science and Art Faculty Department of Mathematics, Malatya, Turkey ,
Abstract :
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?? ? 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 X?? have universal coverings, and a
category UTRGdCov( ?1X ) of coverings of topological ring-groupoid ?1X , in which X and R??0 = X?? 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.
