We prove that if T : X → X is a selfmap of a set X such that ⋂ {T nX : n ∈ N} is a one-point set, then the set X can be endowed with a compact Hausdorff topology so that T is continuous.

In this paper, we prove that, for a given positive number d, if every n + 1 of a collection of compact convex sets in IE contain a set of width d (a set of constant width d, respectively) simultaneously, then all members of this collection contain a set of constant width d1 simultaneously, where d1 = d/ √ n if n is odd and d1 = d √ n+ 2/ (n+ 1) if n is even (d1 = 2d− d √ 2n/(n+ 1), respectively...

We say that X×Y satisfies the Uniquely Universal property (UU) iff there exists an open set U ⊆ X × Y such that for every open set W ⊆ Y there is a unique cross section of U with Ux = W . Michael Hrus̆ák raised the question of when does X × Y satisfy UU and noted that if Y is compact, then X must have an isolated point. We consider the problem when the parameter space X is either the Cantor spac...

Let G ⊂ C be a bounded simply connected domain with boundary Γ and let E ⊂ G be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants: χn = inf p∈Pkn sup q∈Pn−kn ||pq||E ||pq||Γ , n = 1, 2, . . . , where ‖ · ‖K is the supremum norm on a compact set K, Pm is the set of all algebraic polynomials of degree at most m, and kn/n → θ ∈ [0, ...

Let G ⊂C be a bounded simply connected domain with boundary Γ and let E ⊂G be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants: χn = inf p∈Pkn sup q∈Pn−kn ||pq ||E ||pq ||Γ , n = 1,2, . . . , where ‖ ·‖K is the supremum norm on a compact set K ,Pm is the set of all algebraic polynomials of degree at most m, and kn/n→ θ ∈ [0,1] a...

let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

Residue Number System is a numerical system which arithmetic operations are performed parallelly. One of the main factors that affects the system’s performance is the complexity of reverse converter. It should be noted that the complexity of this part should not affect the earned speed of parallelly performed arithmetic unit. Therefore in this paper a high speed converter for moduli set {2n-1, ...

Residue Number System is a numerical system which arithmetic operations are performed parallelly. One of the main factors that affects the system’s performance is the complexity of reverse converter. It should be noted that the complexity of this part should not affect the earned speed of parallelly performed arithmetic unit. Therefore in this paper a high speed converter for moduli set {2n-1, ...

The solvability of the Hausdorff moment problem for an arbitrary compact subset of Euclidean n-space is shown to be equivalent to the nonnegativity of a family of quadratic forms derived from the given moment sequence and the given compact set. A variant theorem for the one-dimensional case and an analogous theorem for the trigonometric moment problem are also given. The one-dimensional theorem...

A first-order expansion of the R-vector space structure on R does not define every compact subset of every Rn if and only if topological and Hausdorff dimension coincide on all closed definable sets. Equivalently, if A ⊆ Rk is closed and the Hausdorff dimension of A exceeds the topological dimension of A, then every compact subset of every Rn can be constructed from A using finitely many boolea...