Simple equations on real intervals (Q1042414)

In contrast to a previous undecidability result of the author [\textit{W. Taylor}, ``Equations on real intervals'', Algebra Univers. 55, No.~4, 409--456 (2006; Zbl 1108.03048)], decidability becomes trivial when the equations to be tested are simple, which means that there is at most one occurrence of some operation symbol on either side: If \(A\) is an absolute retract in the class of all metrizable topological spaces, and if \(S\) is a set of simple equations, then there are continuous operations on \(A\) that satisfy \(S\) if and only if \(S\) is consistent; the consistency of \(S\), however, is equivalent to the existence of a two-element model. The author asserts that some ``very small changes'' in his proof will suffice to obtain the analogous result for the class of all completely regular spaces.