In this chapter, we continue the study of spaces in the class \(\mathfrak {G}\) . We prove that the weak \({ }^{*}\) dual \((E^{\prime },\sigma (E^{\prime },E))\) of a lcs E in the class \(\mathfrak {G}\) is K-analytic if and only if \((E^{\prime },\sigma (E^{\prime },E))\) is Lindelöf if and only if \((E^{\prime },\sigma (E^{\prime },E))\) has countable tightness. We show that every quasibarrelled space in the class \(\mathfrak {G}\) has countable tightness both for the weak and the original topologies. This extends a classical result of Kaplansky for a metrizable lcs. Although \((DF)\) -spaces belong to the class \(\mathfrak {G}\) , concrete examples of \((DF)\) -spaces without countable tightness are provided. On the other hand, there are many Banach spaces E for which E endowed with the weak topology is not Lindelöf. We show, however (following Khurana), that every WCG Fréchet space E is weakly K-analytic. An example due to Pol showing that there exists a Banach space \(C(X)\) over a compact scattered space X such that \(C(X)\) is weakly Lindelöf and not WCG is presented. We show (after Amir and Lindenstrauss) that every non-separable reflexive Banach space contains a complemented separable subspace. Several consequences are provided.