Weakly $(\pi_\mathcal{H},\lambda)$-continuity in Generalized Topologies

Abstract

In this paper, we introduce and study the notions of weakly $\pi$-$\mathcal{H}$-open sets and weakly $(\pi_\mathcal{H})$-continuity in hereditary generalized topological spaces. Also we prove that a function $f:(X,\mu,\mathcal{H})\rightarrow(Y,\lambda)$ is $(\mu,\lambda)$-continuous function if and only if it is weakly $(\pi_\mathcal{H},\lambda)$-continuous function and $(\delta_\mathcal{H},\lambda)$-continuous function where $\mathcal{H}$ is $\mu$-codense.