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.
Khan et al. (Wed,) studied this question.