Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which ...

Two important classes of linear orders that are not σ-scattered are the real types and the Aronszajn types: the real types are those uncountable dense linear orders that are separable; the Aronszajn types are those linear orders that are uncountable and yet have no uncountable suborders that are scattered or real types. This latter class was considered—and proved nonempty—long ago by Aronszajn ...

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...

We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, Jacobian of smooth projective curve over numbers satisfies one-cycles. The main ingredient lift Fourier transform to Chow groups. Similarly, we Tate separable closure finitely generated field. Furthermore, varieties satisfying such are dense i...

Let Sk be the set of separable states on B(C ⊗ C) admitting a representation as a convex combination of k pure product states, or fewer. If m > 1, n > 1, and k ≤ max (m,n), we show that Sk admits a subset Vk such that Vk is dense and open in Sk, and such that each state in Vk has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decomposi...

We study full groups of countable, measure-preserving equivalence relations. Our main results include that they are all homeomorphic to the separable Hilbert space and that every homomorphism from an ergodic full group to a separable group is continuous. We also find bounds for the minimal number of topological generators (elements generating a dense subgroup) of full groups allowing us to dist...

The main goal of this paper is to show that the inductive dimension of a σ-compact metric space X can be characterized in terms of algebraical sums of connectivity (or Darboux) functions X → R. As an intermediate step we show, using a result of Hayashi [9], that for any dense Gδ set G ∈ R the union of G and some k homeomorphic images of G is universal for k-dimensional separable metric spaces. ...

Our main result is a strong boundedness result for the class of separable Rosenthal compacta (that is, separable compact subsets of the first Baire class – see [ADK] and [Ro2]) on the Cantor set having a uniformly bounded dense sequence of continuous functions. We shall denote this class by SRC. The phenomenon of strong boundedness, which was first touched by A. S. Kechris and W. H. Woodin in [...

1. Spaces of piecewise linear maps. Let X and Y be separable polyhedra, X compact and Y locally compact; for the moment let them be connected and of dimension > 0 . Denoting the separable hilbert space of square-summable sequences by h, a space is an kmanifold if separable, metrizable and locally homeomorphic to k. In [4] the author showed that the space C(X, Y) of all continuous maps from X to...

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...