Compact Resolutions and Analyticity.

We consider the large class G of locally convex spaces that includes, among others, the classes of (D F) -spaces and (L F) -spaces. For a space E in class G we have characterized that a subspace Y of (E , σ (E , E ′)) , endowed with the induced topology, is analytic if and only if Y has a σ (E , E ′) -compact resolution and is contained in a σ (E , E ′) -separable subset of E. This result is applied to reprove a known important result (due to Cascales and Orihuela) about weak metrizability of weakly compact sets in spaces of class G. The mentioned characterization follows from the following analogous result: The space C (X) of continuous real-valued functions on a completely regular Hausdorff space X endowed with a topology ξ stronger or equal than the pointwise topology τ p of C (X) is analytic iff (C (X) , ξ) is separable and is covered by a compact resolution. [ABSTRACT FROM AUTHOR]