ABSTRACT
The Gaussian integers are a natural extension of the real numbers, and they have many applications in the areas of number theory. algebraic geometry and quantum mechanics.
The topology of the Gaussian integers is a complex and interesting area of research. There are man) open problems in this area. and the study of these problems is still ongoing. Some of the main things having studied in the set of
Gaussian integ...ers includes:
The set of Gaussian integers is path connected, meaning that any two
Gaussian integers can be connected by a continuous path.
The set of Gaussian integers is not simply connected. meaning that there exists a closed curve in the set of Gaussian integers that cannot be continuously deformed to a point.
The set of Gaussian integers is not compact, meaning that there exists a closed set in the set of Gaussian integers that is not compact.
In this work we also make our humble attempt in the study of the topological properties gaussian integers.
