Research Information System
Filomat, vol.38, no.18, pp.6433-6441, 2024 (SCI-Expanded)
A convergence sequence in a Hausdorff space X has a unique limit. Hence this idea gives us a function which is defined on convergence sequences and has the values in X. Replacing this limit function with any function G whose domain is a certain subset of the sequences extends the notion of limit and such a function G is called G-method. Then sequential definitions of continuity, compactness and connectedness have been extended to G-method setting. In the paper we intent to study some separation axioms such that Ti (i = 0, 1, 2, 3, 4) for G-methods in sets or topological spaces; and characterise them in terms of G-open and G-closed subsets. Then we give some different counterexamples of G-methods and evaluate them if these separations axioms are satisfied.