Compactness via Summability and Sequential Definitions of Connectedness in Neutrosophic Spaces

Abstract

Since the dawn of the mathematical world, countless types of functions have been defined. However, as time passed, each function type became insufficient and different functions were needed to be found. Thereupon, a new type was introduced whose domain was the set of convergent sequences and this new function was named as method. With the help of this new type of function, mathematicians were able to bring different perspectives to the concepts that form the cornerstones of the world of topology as in [4, 9, 10]. This concept was also used in studies on neutrosophic topological spaces and some other different topological spaces. Using the concept of the neutrosophic method introduced earlier, as done in different types of topological spaces, we introduce a new type of sequential compactness and examine its properties. Also, after giving various definitions which constitute the cornerstones of our research and which we think will make important contributions to future studies in neutrosophic spaces, we bring a new perspective to the concept of connectedness, which is among the most important characters of the topology world, based on the concept of the neutrosophic method.