Σ ESR

σ-Normality of Topological Spaces

*-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-Derivations in Banach algebras

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 ...

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...