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TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS | ||
| Iranian Journal of Science | ||
| مقاله 12، دوره 30، شماره 3، اسفند 2006، صفحه 355-362 اصل مقاله (250.36 K) | ||
| نوع مقاله: Research Note | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2006.2775 | ||
| نویسندگان | ||
| A. FATIH OZCAN؛ I. ICEN* ؛ M. HABIL GURSOY | ||
| Inonu University, Science and Art Faculty Department of Mathematics, Malatya, Turkey | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fundamental groupoids؛ topological coverings؛ topological ring-groupoids | ||
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