Insight We are going to explore neutrosophic quasi-normed space. We will define what a neutrosophic quasi-norm is and show an example. As we know, for p ∈ (0,∞) space (‘ P ,d) is a paratopological vector space but it does not possess a norm such that topology generated by this norm is compatible with topology generated by metric d. We give an example that topology generated by neutrosophic quasi norm is compatible with topology generated by metric d. In this paper, we will prove the open mapping theorem and the closed graph theorem for neutrosophic quasi- normed space.

Abstract

We are going to explore neutrosophic quasi-normed space. We will define what a neutrosophic
quasi-norm is and show an example. As we know, for p ∈ (0,∞) space (‘ P ,d) is a paratopological
vector space but it does not possess a norm such that topology generated by this norm is
compatible with topology generated by metric d. We give an example that topology generated
by neutrosophic quasi norm is compatible with topology generated by metric d. In this paper,
we will prove the open mapping theorem and the closed graph theorem for neutrosophic quasi-
normed space.