@article { author = {FATIH OZCAN, A. and ICEN, I. and HABIL GURSOY, M.}, title = {TOPOLOGICAL RING-GROUPOIDS AND LIFTINGS}, journal = {Iranian Journal of Science}, volume = {30}, number = {3}, pages = {355-362}, year = {2006}, publisher = {Springer}, issn = {2731-8095}, eissn = {2731-8109}, doi = {10.22099/ijsts.2006.2775}, abstract = {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.}, keywords = {Fundamental groupoids,topological coverings,topological ring-groupoids}, url = {https://ijsts.shirazu.ac.ir/article_2775.html}, eprint = {https://ijsts.shirazu.ac.ir/article_2775_f612489b5f4ee6a241d045d959f7d698.pdf} }