International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/647 2020 2020 Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R& D Institute of Science and Technology, Chennai, Tamil Nadu, India admin admin The new concepts of a neutrosophic Gδ set and neutrosophic Gδ-α-locally closed sets are introduced. Also, a neutrosophic εGδ-α-locally quasi neighborhood, neutrosophic Gδ-α-locally continuous function, neutrosophic Gδ-α-local T2 space, neutrosophic Gδ-α-local Urysohn space, neutrosophic Gδ-α-local connected space, and neutrosophic Gδ-α-local compact space are discussed and some interesting properties are established. 2021 2021 61 65 10.54216/IJNS.130202 https://www.americaspg.com/articleinfo/21/show/647