  For classes of topological vector spaces, we analyze under which conditions
open-mapping, continuous-inverse, and closed-graph properties are equivalent.
Here, closure under quotients with closed subspaces and closure under closed
graphs are sufficient.
  We show that the class of barreled Ptak spaces is exactly the largest class
of locally-convex topological vector spaces, which contains all Banach spaces,
is closed under quotients with closed subspaces, is closed under closed graphs,
is closed under continuous images, and for which an open-mapping theorem, a
continuous-inverse theorem, and a closed-graph theorem holds.
  An analogous, weaker result also holds for the strictly larger class of
barreled infra-Ptak spaces.
