Montel (DF)-Spaces, Sequential (LM)-Spaces and the Strongest Locally Convex Topology
Montel (DF)-Spaces, Sequential (LM)-Spaces and the Strongest Locally Convex Topology
Topologists say that a space is sequential if every sequentially closed set is closed. Directly from the definitions, metrizable ⇒ Fréchet–Urysohn ⇒ sequential ⇒ k-space. Kąkol showed that for an (LM)-space (the inductive limit of a sequence of locally convex metrizable spaces), metrizable, Fréchet–Urysohn. The Cascales and Orihuela result that …