Study on topological properties of Pythagorean Neutrosophic Normed Space

Abstract

We introduce the concept of Pythagorean neutrosophic normed spaces. We study that every Pythagorean neutrosophic normed space need not to be neutrosophic normed space. We define convergence of a sequence in Pythagorean neutrosophic normed spaces and Cauchy sequence. We define open ball, boundedness and compact with respect to PNNS. We induce a topology generated by these open balls. We prove that topology generated by these balls is Hausdorff.