Compatibility of spaces and equations
by
Walter Taylor
University of Colorado

A (finite or infinite) set S of equations, in operation symbols F_t (t Î T) and variables x_i, is said to be compatible with a topological space A iff there exist continuous operations F_t^A on A such that the algebra A=(A;F_t^A)_{t Î T} satisfies the equations S.

We discuss compatibility, and include fairly easy sketches of two results. (1) If n ¹ 1, 3, 7 then the only theories S compatible with Sⁿ (the n-sphere) are trivial theories (in a sense to be made precise). (2) There is no algorithm to decide R-compatibility for all finite S.

Date received: July 6, 2004

Copyright © 2004 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 # caoc-13.