Abstract
The purpose of this work is to construct a new crossover operator using the properties of DNA and RNA by using topological concepts in constructing flexible mathematical models in the field of biomathematics. Also, we investigate and study topological properties of the constructed operators and the associated topological spaces of DNA and RNA. Finally we use the process of exchange for sequence of genotypes structures to construct new types of topological concepts to investigate and discuss several examples and some of their properties.