Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X. Let S, T be semilattices. One can check that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bou...

We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges. Kergin interpolation is a generalization of both Lagrange interpolation in the one dimensional case, and the Taylor polynomial in the case where all interpolation points coincide. In several vari...

Let E and F be Banach lattices and assume E∗ has no atoms. Let T : E → F be a norm bounded disjointness preserving operator from E into F . Then β(T ) = α(T ) = ‖T‖e = ‖T‖.

Let R(·) stand for the bounded-error randomized query complexity. We show that for any relation f ⊆ {0, 1}×S and partial Boolean function g ⊆ {0, 1}×{0, 1}, R1/3(f ◦g ) = Ω(R4/9(f)·

It is shown that strict resolutions of Fn by F–limit groups have length bounded by 3n. As an application we show that the abelian analysis lattice of a limit group L has height bounded by 3 rk(L).

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

208 NOTICES OF THE AMS VOLUME 51, NUMBER 2 As far as I know, the notion of a quasi-morphism does not have much to do with category theory. This very natural idea underlies several interesting recent developments at the crossroads of algebra, topology, geometry, and dynamics. Other, perhaps better, names currently in use for the same concept are quasi-homomorphism and pseudo-character. Let G be ...

where Ω ⊂ R (N ≥ 1) is a bounded smooth domain, λk is an eigenvalue of the problem −Δu = λu in Ω, u = 0 on ∂Ω, and f : Ω × R → R is a Carathéodory function. If f(x, 0) = 0 for a.e. x ∈ Ω the constant u = 0 is a trivial solution of the problem (P). In this case, the key point is proving the existence of nontrivial solutions for (P). For this purpose, we need to introduce some conditions on the b...

System F ! is an extension of system F ! with subtyping and bounded quantiication. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed-calculus with subtyping, bounded quan-tiication and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show t...

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...