On Extension of Metricspace to Neutro Hypermetricspace

Polvan introduced the impression of strong neutro metricspaces. He demonstrtated this impression depending on the neutro precepts from the neutro function one of the impressions of Smarandache. In this study, we introduce an extension of neutro metricspaces as neutro hypermetricspaces and investigated their qualities. We show that neutro hypermetricspaces are an extension of metricspaces and analyzed the relations between metricspaces and neutro hypermetricspaces. The basic impressions such as open positive-ball subsets and open negative-ball subsets are defined and are presented by some finite and finite neutro hypermetricspaces. Based on the open positive-ball subsets and open negative-ball subsets, we demonstrate the impressions of neutro negative-open sets and neutro positive-open sets, respectively