Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

La Classe Borélienne Ne Détermine Pas Le Type Topologique De Cp(x)

We prove that, for every countable ordinal α ≥ 3, there exists countable completely regular spaces Xα and Yα such that the spaces Cp (Xα ) and Cp (Yα ) are borelian of class exactly Mα , but are not homeomorphic.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Criterion of Normality of the Completely Regular Topology of Separate Continuity

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.