A note on dense subspaces in separable Fréchet spaces (Q1090885)

It is proved that every infinite dimensional separable Fréchet space X contains a dense subspace of infinite codimension E such that: (1) dim E\(=2^{\aleph}\) and E admits a finer locally convex ultrabarrelled topology. (2) E does not admit any locally convex topology comparable with the original one for which E is an unordered Baire-like space.