Bezdek, KárolyRobock, Nathan2019-09-172019-09-172019-09-13Robock, N. (2019). From Convexity to R-Convexity (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/110989This thesis will give a brief overview of some classical theorems of convexity, such as those of Tietze and Nakajima, which allow us to determine convexity based on local neighbourhoods of boundary points, and then proceed to introduce the concept of spindle convexity and r-convexity. I will then prove analogues of these important classical theorems for r-convexity, if possible. Lastly, I will go through two-point symmetrization for both convexity and r-convexity, and prove some new results for the r-convexity version of two-point symmetrization.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Discrete GeometryGeometryTopologyR-convexitycombinatoricsEducation--Mathematicsmaster thesis10.11575/PRISM/37054