TY - JOUR ID - 2775 TI - TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS JO - Iranian Journal of Science JA - ISTT LA - en SN - 2731-8095 AU - FATIH OZCAN, A. AU - ICEN, I. AU - HABIL GURSOY, M. AD - Inonu University, Science and Art Faculty Department of Mathematics, Malatya, Turkey Y1 - 2006 PY - 2006 VL - 30 IS - 3 SP - 355 EP - 362 KW - Fundamental groupoids KW - topological coverings KW - topological ring-groupoids DO - 10.22099/ijsts.2006.2775 N2 - We prove that the set of homotopy classes of the paths in a topological ring is a topological ringobject (called topological ring-groupoid). Let p : Xô€€„ → 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 Xô€€„ have universal coverings, and acategory UTRGdCov( π1X ) of coverings of topological ring-groupoid π1X , in which X and Rô€€„0 = Xô€€„ haveuniversal coverings, and then prove the equivalence of these categories. We also prove that the topologicalring structure of a topological ring-groupoid lifts to a universal topological covering groupoid. UR - https://ijsts.shirazu.ac.ir/article_2775.html L1 - https://ijsts.shirazu.ac.ir/article_2775_f612489b5f4ee6a241d045d959f7d698.pdf ER -