This chapter deals with several concepts related with networks with applications both in Topology and Functional Analysis. Especially we will discuss this concepts for topological groups with \(\mathfrak {G}\) -bases. Recall that topologists are seeking several possible general sequential concepts, which together under an additional topological condition, force a topological space X to be metrizable. Following this line of research Tsaban and Zdomskyy introduced a property (the strong Pytkeev property) which implies the countable tightness, and in the frame of Fréchet–Urysohn topological groups yields the metrizability.