Outtopological Digraph Space and Some Related Properties

Abstract

The outtopological digraph space, a novel topological constraint imposed by a subbasis, is introduced in this work. A subbasis $\overleftarrow{\textrm{I}}^{\alpha}_{\underset{\cdot}{e}}$ is a set contains one vertex such that the edge ẹ is outdegree of it. As a result, various theorems have been established. A characterization and some examples are provided to describe this new structure.