On linear continuous open surjections of the spaces Cp (X) Academic Article uri icon

abstract

  • Solving a problem by Arkhangel'skiĭ, we construct a linear continuous open surjection L : Cp(X) → CP(Y) for compacta X and Y with 0 < dim X < dim Y < ∞. An example of nonopen linear continuous surjection of the space Cp[0, 1] onto itself is given. Related topics and results are discussed.

publication date

  • January 1, 1997