A Study on generalized sequential continuity

Let 𝑋 be a Hausdorff topological group which satisfies the first countability axiom. The limit of a sequence in 𝑋 defines a function denoted by lim from the set of all convergent sequences in 𝑋 to 𝑋. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional 𝐺 defined on a linear subspace of the vector space of all real sequences. Recently, Çakallı has extended this concept to the topological group setting and introduced the concepts of 𝐺−sequential compactness, 𝐺−sequential continuity and sequential connectedness. However, during this extension process, the concept of 𝐺−sequential continuity is given only for the functions defined on a set 𝑋 to itself. In this thesis study we introduce and give a further investigation of 𝐺−𝐻−sequential continuity in topological groups which satisfy the first countability axiom. In the fifth chapter, the results obtained in the thesis are discussed and some suggestions are given for new studies.