ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 54 Chatyrko, V. A., Linköping University, Sweden, On infinite-dimensional Cantor manifolds The following is a joint work with E. Pol. Our spaces are metrizable separable. A space is hereditarily strongly infinite-dimensional ( h. s. i. d.) if every its subspace is either 0-dimensional or strongly infinite-dimensional. The first example of a h. s. i. d. compactum was given by Rubin. A nontrivial continuum is an infinite-dimensional Cantor manifold if all closed sets which disconnect it are infinite-dimensional. Theorem. There is a family of continuum many h. s. i. d. Cantor manifolds such that for every two spaces from this family, no open subset of one is embeddable into the other. Reference: V. Chatyrko, and E. Pol, Continuum many Fréchet types of hereditarily strongly infinite-dimensional Cantor manifolds, Warsaw University P 98-01 (13) 1998