The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...

We describe a process for defining and computing a fundamental domain in the upper half plane H of a Shimura curve X 0 (N) associated to an order in a quaternion algebra A/Q. A fundamental domain for X 0 (N) realizes a finite presentation of the quaternion unit group, modulo units of its center. We give explicit examples of domains for the curves X 0 (1), X 0 (1), and X 35 0 (1). The first exam...

The focus of this exposition is the fundamental group of a topological space. The paper begins by defining paths and homotopy, and proceeds to construct the fundamental group. Later, attention turns to the consequences of the construction, in particular to the fundamental group of S1 and Van Kampen’s Theorem.

This is the next article in a series devoted to the homotopy theory (following [11] and [12]). The concept of fundamental groups of pointed topological spaces has been introduced. Isomorphism of fundamental groups defined with respect to different points belonging to the same component has been stated. Triviality of fundamental group(s) of R n has been shown. the terminology and notation for th...