On the orbits of ξ Scorpii, Σ 2173, Σ 3121, and μ2 Herculis

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...

σ-Normality of Topological Spaces

On effective σ-boundedness and σ-compactness

We prove several dichotomy theorems which extend some known results on σ -bounded and σ -compactpointsets. In particular we show that, given a finite number of Δ1 equivalence relations F1 , . . . , Fn , any Σ1 set A of the Baire space either is covered by compact Δ1 sets and lightface Δ1 equivalence classes of the relations Fi , or A contains a superperfect subset which is pairwise Fi -inequiva...

Covering Σ 0 ξ - generated ideals by Π 0 ξ sets

We develop the theory of topological Hurewicz test pairs: a concept which allows us to distinguish the classes of the Borel hierarchy by Baire category in a suitable topology. As an application we show that for every Πξ and not Σ 0 ξ subset P of a Polish space X there is a σ-ideal I ⊆ 2 such that P / ∈ I but for every Σξ set B ⊆ P there is a Πξ set B′ ⊆ P satisfying B ⊆ B′ ∈ I. We also discuss ...

σ-ring and σ-algebra of Sets1

In this article, semi-ring and semi-algebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semi-ring of sets has already been formalized in [12], that is, strictly speaking, a definition of a quasi semi-ring of sets suggested in the last few decades [14]. We adopt a classical definition of a semi-ring of sets here to avoid such a confusion. Ring ...