The Equivariant Universality and Couniversality of the Cantor Cube
by
Tzvi Scarr
Jerusalem College of Technology, Jerusalem, ISRAEL
Coauthors: Michael Megrelishvili (Bar-Ilan University, ISRAEL)

Let <G, X, \alpha> be a G-space, where G is non-Archimedean and second countable, and X is compact, metrizable, and zero-dimensional. Let <H({0, 1}^\aleph₀), {0, 1}^\aleph₀, \tau> be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then

1. there exists a topological group embedding j:G \hookrightarrow H({0, 1}^\aleph₀);
2. there exists an embedding \psi:X \hookrightarrow {0, 1}^\aleph₀, equivariant with respect to j, such that \psi(X) is a G-retract of {0, 1}^\aleph₀ with respect to j and \psi.

Date received: May 4, 2000

Copyright © 2000 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 # caeh-09.