Coincidence theorems for involutions

Scepin (1974) and Izydorek and Jaworowski (1995, 1996) showed that for each k and n such that 2k > n there exists a contractible k-dimensional simplicial complex Y and a continuous map phi:S-n --> Y without the antipodal coincidence property, i.e., phi(x) not equal phi(-x) for all x is an element of S-n. On the other hand, if 2k less than or equal to n then every map phi:S-n --> Y to a k-dimensional simplicial complex has an antipodal coincidence point. In this paper it is shown that, with some minor modifications, these results remain valid when S-n and the antipodal map are replaced by any normal space and an involution with color number n + 2. (C) 1998 Elsevier Science B.V.