Application of selection principles in the study of the properties of function spaces

作者：Osipov A V^*

来源：Acta Mathematica Hungarica, 2018, 154(2): 362-377.

DOI：10.1007/s10474-018-0800-4

• strongly sequentially separable
• sequentially separable
• function space
• selection principle
• Gerlits-Nagy gamma property
• Baire function
• sigma-set
• S1(Omega, Gamma)
• S-1( B-Omega, B-Gamma)
• gamma-set
• C-p space
• b-Sierpinski set

For a Tychonoff space X, we denote by C (p) (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence.
In this paper we prove that:
If every finite power of X is Lindelof then C (p) (X) is strongly sequentially separable iff X is gamma-set.
B-alpha (X) (= functions of Baire class () on a Tychonoff space X with the pointwise topology) is sequentially separable iff there exists a Baire isomorphism class from a space X onto a -set.
B-alpha (X) is strongly sequentially separable iff and X is a -cover -set for 0 < alpha <= omega(1).
There is a consistent example of a set of reals X such that C (p) (X) is strongly sequentially separable but B (1)(X) is not strongly sequentially separable.
B(X) is sequentially separable but is not strongly sequentially separable for a -SierpiA"ski set X.

• 出版日期2018-4