Preservation of Topological Properties under Some Maps

In this paper, we investigate the preservation of some topological properties during the weakly discontinuous, scatteredly continuous, and point-wise discontinuous maps on topological spaces. In addition, we also investigate the preservation of topological properties during such corresponding homeomorphisms. Furthermore, we also establish some significant relationships among weakly discontinuous, scatteredly continuous, and point-wise discontinuous maps. Scatteredly continuous map, weakly discontinuous map, point-wise discontinuous map, weak homeomorphism, scattered homeomorphism, point-wise homeomorphism.