Akademik Veri Yönetim Sistemi
6th International Conference of Mathematical Sciences, ICMS 2022, Hybrid, Istanbul, Türkiye, 20 - 24 Temmuz 2022, cilt.2879
One can notice that if a topological space X is a Hausdorff, then the limits of the sequences in X lead to a function defined on set consisting of all sequences in X converging to a point in X. The range of the function is X; and some topological concepts such as open subsets, closed subsets, closure and accumulation points, continuous functions and many others in the first countable spaces can be stated in terms of convergent sequences. The concept of limit was developed not only for topological spaces but also for sets by any function G which is defined on a subset of the sequences in X with range X which is not only a topological space but also a set; and then G-continuity, G-compactness and G-connectedness have been studied by several authors. These notions produce the usual notions of topological spaces provided that the space X is first countable and Hausdorf, and the function G is lim. In this paper we define some counter examples of convergent G-methods and characterise G-open, G-closed subsets associated with these G-convergent methods; and then consider the G-continuous, G-open and G-closed functions.