Universal graphs and universal functions

Universal graphs and functions on ω1

It is shown to be consistent with various values of b and d that there is a universal graph on ω1. Moreover, it is also shown that it is consistent that there is a universal graph on ω1 — in other words, a universal symmetric function from ω 1 to 2 — but no such function from ω 2 1 to ω. The method used relies on iterating well known reals, such as Miller and Laver reals, and alternating this w...

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Universal Approximator Property of the Space of Hyperbolic Tangent Functions

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.

Universal Functions

A function of two variables F (x, y) is universal if for every function G(x, y) there exists functions h(x) and k(y) such that G(x, y) = F (h(x), k(y)) for all x, y. Sierpiński showed that assuming the Continuum Hypothesis there exists a Borel function F (x, y) which is universal. Assuming Martin’s Axiom there is a universal function of Baire class 2. A universal function cannot be of Baire cla...

FLOWS AND UNIVERSAL COMPACTIFICATIONS

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...