A GT genarated by a family of maps

Abstract

‎In this paper we define weak and strong generalized topologies‎. ‎We show that a large range of generalized topological spaces can be characterized by the weak and strong generalized topologies‎. ‎As a main result‎, ‎we prove that a GTS is completely $\mu$-regular if and only if $\mu$ is the weak GT generated by the family $C^{*}_{\mu,\nu}(X)$ of all $(\mu,\nu_\mathbb{R})$-continuous functions‎.