Generalized Topological Groupoids

Abstract

Our aim in this paper is to give the notion of generalized topological groupoid which is a generalization of the topological groupoid by using the notion of generalized topology defined by Csasz ´ ar [6]. We in- ´ vestigate the basic facts in the groupoid theory in terms of generalized topological groupoids. We present the action of a generalized topological groupoid on a generalized topological space. We obtain some characterizations about this concept that is called the generalized topological action. Beside these, we give definition of a generalized topological crossed module by generalizing the concept of crossed module defined on topological groupoids. At the last part of the study, we show how a generalized topological crossed module can be obtained from a generalized topological groupoid and how a generalized topological groupoid can be obtained from a generalized topological crossed module.

The Transformation of the Evolute Curves Using Lifts on R^3 to Tangent Space Tr^3

“…extended manifolds) using the lift function [1][2][3][4][5][6]. Thus, it may be extended the following theorem given on space to its tangent space (see extended frames and curves [7][8][9][10][11]). The evolution of a given curve is a well-known concept in…”