On nano Penta topological spaces

The main purpose of this paper was to tender a new type of topology which named Nano Penta Topology (briefly NP-topology), by studying three cases independent from each other, depending on the number of equivalence relations of universe set and its subsets , supporting the study by examples and cases with some properties related to these concepts. We also set a situation on the lower and upper approximations for the third case (using five equivalence relations defined on the universe set and its subsets) , that is generalize a topological space which called Penta Multi-Granular Nano Topological Space, briefly (M_GNPT). Basic properties of such topologies were discussed with suitable examples. So be Nano Penta (Penta Multi- Granular Nano) extremally disconnected with some properties were studied.