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...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.

This paper presents an extended model for describing topological relations between two sets (objects) in geographic information systems (GIS). First, based on the definition of the topological relations between two objects, we uncover a sequence of topological relations between two convex sets. Second, an extended model for topological relations between two sets is proposed based on the new def...

Homomorphisms h:F ! * G are studied, where F is a free group and * G is the free product. In Part I, the conditions imposed on the homomorphism h relate to certain commutators in F . The method of proof is to obtain a topological realization of h, interpreting F as the fundamental group of a surface with boundary and * G as the fundamental group of a wedge of complexes. Standard general positio...

Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

The notion of minimal set is centrally located in topological dynamics. Topological dynamics may be defined as the study of transformation groups with respect to those properties, wholly or largely topological in nature, whose prototype occurred in classical dynamics. Henri Poincaré was the first to introduce topological notions and methods in dynamics, that is, the study of ordinary differenti...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

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...