On complemented subspace of convergence-free spaces

Abstract

The author proved in 1935 (Math. Annalen 111,229-258) that two convergence-free spaces $λ₁$ and $λ₂$, of countable degree are isomorphic if and only if there exists a perturbation of the coordinates which transforms $λ₁$ , into$λ₂$. The author gives a ne w exposition of this result and its consequences and formulates some unsolved problems on the structure of the complemented subspaces of spaces of countable degree.