We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set A, in the Effros-Borel space of subspaces of C[0, 1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y , with a Schauder basis, that contains isomorphic copies of every space X in the c...

We prove that a separable Hausdorff topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2. In this paper we construct a scattered compact space admitting no continuous mean operation, thus answering Problem 5 of [4]. By a mean operation on a set X we understand any binary operation...

A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of the Euclidean plane, and some explicit examples are constructed. Finally a conjecture on possible generalizations to other classes of systems is discussed: i...

In this brief note, we prove that every space is a sequence-covering image of a topological sum of convergent sequences. As the application of this result, sequence-covering images of locally compact metric spaces (or, locally separable metric spaces, metric spaces) and sequentially-quotient images of a locally compact metric spaces (or, locally separable metric spaces, metric spaces) are equiv...

In this paper we obtain an integral characterization of a two-slded upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jaln and Taylor [2] where B n. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3] The special case that when B is itself a real separable Hilbe...

De Groot proved that every group is the autohomeomorphism group of some metrizable space. A space is totally disconnected if every connected subset of it contains at most one point. We prove that every separable metrizable totally disconnected topological group is topologically isomorphic to the autohomeomorphism group of some separable metrizable space, when given the compact-open topology. It...

Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that “most” functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive...

0 g(s, x(s), x(s− τ(s))) (t− s)1−α dω(s), t ∈ J = [0, T ], x(t) = ψ(t), t ∈ [−r, 0], (1.1) where 0 < α ≤ 1, T > 0 and A is a linear closed operator , defined on a given Hilbert space X . It is assumed that A generates an analytic semigroup S(t), t ≥ 0. The state x(.) takes its values in the Hilbert spaceX , and the control function u(.) is in L2(J, U), the Hilbert space of admissible control fu...

We prove that the Covering Property Axiom CPAprism, which holds in the iterated perfect set model, implies the following facts. • There exists a family G of uniformly continuous functions from R to [0, 1] such that |G| = ω1 and for every S ∈ [R] there exists a g ∈ G with g[S] = [0, 1]. • The additivity of the Marczewski’s ideal s0 is equal to ω1 < c. 1 Preliminaries and axiom CPAprism Our set t...