首页|P-spaces and an unconditional closed graph theorem
P-spaces and an unconditional closed graph theorem
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NETL
NSTL
Let X be a completely regular (Tychonoff) space, and let C(X), U(X), and B_1(X) denote the sets of all real-valued functions on X that are continuous, have a closed graph, and of the first Baire class, respectively.We prove that U(X) = C(X) if and only if X is a P-space (i.e., every G_δ-subset of X is open) if and only if B_1 (X) = U(X). This extends a list of equivalences obtained earlier by Gillman and Henriksen, Onuchic, and Iseki. The first equivalence can be regarded as an unconditional closed graph theorem; it implies that if X is perfectly normal or first countable (e.g., metrizable), or locally compact, then there exist discontinuous functions on X with a closed graph. This complements earlier results by Dobos and Baggs on discontinuity of closed graph functions.
real-valued functions with a closed graphpoints of discontinuitycompletely regular or P-spacesbaire functions
Marek Wojtowicz、Waldemar Sieg
展开 >
Instytut Matematyki, Uniwersytet Kazimierza Wielkiego, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
NETL
NSTL
