On a new variant of I-convergence in topological spaces

Abstract

In this write-up, we mainly introduce b-I-convergence of sequences, b-convergence and b-Iconvergence of nets in topological spaces, and put forward some important topological investigations. Existence of b-ω-accumulation point is presented via admissible ideal and b-I-cluster point of sequence. It is shown that a map f : Z → W is quasi-b-irresolute if and only if for every net (s_d)_d∈D converging to zo, the image net (f(s_d)_d∈D) b-converges to f(z_o). Notion of b-I-cluster point of net is disclosed along with its a nice characterization as: ‘Corresponding to a given net s : D → Z, there exists a filter G on Z such that z_o ∈ Z is a b-I-cluster point of the net (s_d)_d∈D if and only if z_o is a b-cluster point of the filter G’. Another characterizationof b-I-cluster point of net with respect to a certain type of class of subsets is demonstrated. Further, we show that b-I-cluster point of a net in a b-compact space always exist.