Atlas home || Conferences | Abstracts | about Atlas

Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

View Abstracts
Conference Homepage

On Spaces with Finite Basic Families
by
Ziqin Feng
University of Pittsburgh
Coauthors: Paul Gartside

Implicit in Kolmogorov's solution of Hilbert's 13th Problem is the notion of a (finite) basic family. A family Phi1, ..., Phin of continuous maps of a space X to the reals is basic if for every continuous real valued function f on X there are continuous maps g1, ..., gn of the reals to the reals such that f(x) = g1(Phi1(x))+ ... + gn(Phin(x)) for all x in X.

Giving complete answers to questions of Sternfeld and Hattori we characterize completely spaces with a basic family as follows:

a Tychonoff space X has a finite basic family if and only if it is finite dimensional, locally compact and separable metrizable.

Date received: February 26, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawk-83.