Dismountable and non-Dismountable Spaces via Proximity Space

Abstract

Most problems studied by researchers were converted into mathematical formulas in the proximity space because this space is easily employed to solve the different problems of life. Therefore, the current study attempts to find a new property for proximity spaces using the proximity and cluster properties and linking them to obtain new cumulative points, it is called the Bushy Points and the set of all these points is the Bushy set. They form a coherent mathematical foundation for the topological formula that is looking for, which can be called dismountable space. If the space does not have this property, it can be called a non-dismountable space.