We present an example of a metrizable space having the separable extension property but which is not an Absolute Neighborhood Retract.
We present an example of a metrizable space having the separable extension property but which is not an Absolute Neighborhood Retract.
Continuing previous investigations concerning Bernstein polynomials, the purpose of this paper is to establish the weak-type inequality (f∈Lp(0,1),n∈ℕ)in terms of the Kantorovitch polynomial Kkƒ and the modulus of continuity (ϕ2(x): = x(1 − x))Such estimates which immediately imply well-known inverse results are also obtained for the Kantorovitch version of the Szász-Mirakjan and Baskakov operators, respectively.
We consider partitions of ℝ16 into pairwise complementary 8-dimensional subspaces whose union covers ℝ16 (or, equivalently, fiberings of %plane1D;4AE;15 by great 7-spheres). It is shown that if such a partition is (globally) invariant by a closed subgroup of GL16(ℝ) locally isomorphic to SO7(ℝ,1), then it is linearly equivalent to the classical Hopf partition corresponding to the Cayley numbers %plane1D;4AA;, namely the system of lines through the origin in the affine Cayley plane over %plane1D;4AA;.
Let S be a hypersurface in Pn (n≧3) with only normal crossings and let ƒ : XPn be a finite ramified covering which is unramified over Pn − S. Then S. Kawai has shown that there are neither regular 1-forms nor regular 2-forms on X. The aim of this article is to derive a stronger conclusion: H0(X,ΩXp)= 0 for 1≦p<n , and moreover H0(X,ΩXp)= 0 if deg S≦n+1.
In this note we use a “normal form”, due to Sylvester, for the equation of a generic cubic surface in ℙ3(ℂ) to prove that %plane1D;4B0;= {moduli space of pairs (S,P) with S smooth cubic surface, P a point on S} is rational. We then prove that %plane1D;510;3oth = {moduli space of curves of genus three together with one odd theta-characteristic} is birational to %plane1D;4B0; and so rational.
Let K be a non-archimedean, non trivially valued, complete field. Given a dual pair of vector spaces (E, F) over K we study the finest locally convex topology of countable type %plane1D;4A5; on E such that (E%plane1D;4A5;′= F and, given a locally convex space E, %plane1D;4A5; we describe the finest topology of countable type on E coarser than %plane1D;4A5; It is also shown how the class (S0) of spaces of countable type can be obtained from an operator ideal.
Every completely distributive complete lattice is a subdirect product of copies of the lattice {0, 1} and the real unit interval.
Let C(X,E) be the space of all continuous functions from an ultraregular space X to a non-Archimedean locally convex space E. Necessary and/or sufficient conditions are given so that C(X,E), with the topology of uniform convergence on compact sets or with the topology of simple convergence, is bornological or c-ultrabornological.