Neutrosophic compactness via summability and sequential definitions of connectedness in neutrosophic spaces

Abstract

In this study, using the concept of the neutrosophic method introduced earlier, as done in different types of topological spaces, a new type of sequential compactness is introduced and investigated. After giving various definitions which constitute the cornerstones of our research, in the third section, a new perspective to the concept of connectedness is brought, which is among the most important characters of the topology world, based on the concept of the neutrosophic method. By giving examples of each new definition given in the second and third sections, a better understanding of the new concepts given is provided.