ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 55P55 Ivanšić, Ivan, University of Zagreb, Croatia and Rubin, Leonard R., University of Oklahoma, U. S. A. Borsuk’s Index and Pointed Movability for Projective Movable Continua It is shown that each projective movable continuum X is shape dominated by a regularly movable continuum of the same dimension. This has two consequences. First, if the dimension of X is ≤ k, k ≠ 2, then X is shape dominated by a continuum in R^{2k}. This answers affirmatively a special case of a question raised by Borsuk, at least as far back as 1975, in all dimensions except dim = 2. Second, it implies that such a continuum is pointed movable, again giving an affirmative answer, in a special case, to the old question in shape theory of whether movable continua are always pointed movable.