Locally Constant Functions
by
Joan Hart
University of Wisconsin
Coauthors: Kenneth Kunen

Let X be a compact Hausdorff space and M a metric space. E₀(X, M) is the set of f in C(X, M) such that there is a dense set of points x in X with f constant on some neighborhood of x. We describe some general classes of X for which E₀(X, M) is all of C(X, M). These include \betaN \N, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. We also build three first countable Eberlein compact spaces, F, G, H, with the following properties: For all metric M, E₀(F, M) contains only the constant functions, and E₀(G, M) = C(G, M). If M contains the Hilbert cube, then E₀(H, M) =/= C(H, M); but E₀(H, M) = C(H, M) whenever M subset or equal Rⁿ for some finite n. F, G, H contain no isolated points.

Date received: April 12, 1996

Copyright © 1996 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 # caae-30.