In the present paper, we will propose the novel notions (e.g., Qp-closed set, Qp-open set, Qp-continuous mapping, Qp-open
mapping, and Qp-closed mapping) in topological spaces. ,en, we will discuss the basic properties of the above notions in detail.
,e category of all Qp-closed (resp. Qp-open) sets is strictly between the class of all preclosed (resp. preopen) sets and gp-closed
(resp. gp-open) sets. Also, the category of all Qp-continuity (resp. Qp-open (Qp-closed) mappings) is strictly among the class of all
precontinuity (resp., preopen (preclosed) mappings) and gp-continuity (resp. gp-open (gp-closed) mappings). Furthermore, we
will present the notions of Qp-closure of a set and Qp-interior of a set and explain some of their fundamental basic properties.
Several relations are equivalent between two different topological spaces.,enovel two separation axioms (i.e., Qp-R0 and Qp-R1)
based on the notion of Qp-open set and Qp-closure are investigated. ,e space of Qp-R0 (resp., Qp-R1) is strictly between the
spaces of pre-R0 (resp., pre-R1) and gp-Ro (resp., gp-R1). Finally, some relations and properties of Qp-R0 and Qp-R1 spaces
are explained.