On homotopic distance

The aim of this thesis is to introduce homotopic distance with its properties and show homotopic distance as pseudometric thanks to some properties of homotopic distance. Homotopic distance is first introduced by Macias-Virgos and Mosquera-Lois. Homotopic distance is a generalization of topological complexity and Lusternik-Schnirelmann category. In the first chapter of the thesis, it is mentioned that topological spaces are examined with an algebraic approach and connection between algebraic topology and homotopy. The basic notions that help to understand the notions in the third, fourth and fifth chapters of thesis are introduced in the second chapter. Homotopy which is necessary to define homopic distance is given in the third chapter. In the fourth chapter, the definition of homopotic distance is given and the relation between topological complexity and Lusternik-Schnirelmann category with homotopic distance is given. Moreover, some properties of homotopic distance are given in that chapter. In the fifth chapter, pseudometric spaces induced by homotopic distance are given.