Certain aspects of ideal convergence in topological spaces

Abstract In this note we investigate certain aspects of ideal convergence of functions, in a very general context. We consider the situation, given an arbitrary infinite set S, free ideals I , K ( ⊂ I ) and a family F ⊂ [ S ] ≥ ω , when an I convergent function f from S to a topological space X will have a F -subfunction which is K convergent to the same limit. We present certain observations on such topological spaces. Further we also introduce the notion of I -cluster points of functions and make some observations.