In this chapter, we show that a tvs that is a Baire space and admits a countably compact resolution is metrizable, separable, and complete. We prove that a linear map \(T:E\rightarrow F\) from an F-space E having a resolution \(\{K_\alpha :\alpha \in \mathbb {N}^{\mathbb {N}}\}\) into a tvs F is continuous if each restriction \(T|K_\alpha \) is continuous. This theorem (due to Drewnowski) was motivated by Arias de Reyna–Valdivia–Saxon’s theorem about non-Baire dense hyperplanes in Banach spaces. We provide a large class of weakly analytic metrizable and separable Baire tvs that are not analytic (clearly such spaces are necessarily not locally convex).