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( π1X ) of coverings of topological ring-groupoid π1X , in which X and R0 = 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.
FATIH OZCAN, A., ICEN, I., & HABIL GURSOY, M. (2006). TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS. Iranian Journal of Science, 30(3), 355-362. doi: 10.22099/ijsts.2006.2775
MLA
A. FATIH OZCAN; I. ICEN; M. HABIL GURSOY. "TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS", Iranian Journal of Science, 30, 3, 2006, 355-362. doi: 10.22099/ijsts.2006.2775
HARVARD
FATIH OZCAN, A., ICEN, I., HABIL GURSOY, M. (2006). 'TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS', Iranian Journal of Science, 30(3), pp. 355-362. doi: 10.22099/ijsts.2006.2775
VANCOUVER
FATIH OZCAN, A., ICEN, I., HABIL GURSOY, M. TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS. Iranian Journal of Science, 2006; 30(3): 355-362. doi: 10.22099/ijsts.2006.2775
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