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Spring Topology and Dynamical Systems Conference
March 15-17, 2001
Centro de Convenciones
Morelia City, Michoacán, Mexico

Organizers
Alejandro Illanes, Sergio Macías, Jesus Muciño, María Luisa Pérez

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More non-analytic families of continua.
by
Pawel Krupski
University of Wroclaw, Poland and UNAM, Mexico

The method of [U. Darji, Complexity of hereditarily decomposable continua, Topology Appl. 103 (2000), 243-248] is extended and many subsets of the hyperspace of all subcontinua of the cube In, n > 1, are revealed to be non-analytic. For example,

  1. the family of all continua in In, n > 1 (n > 2), that admit only arcs (simple closed curves) as chainable (circularly chainable) subcontinua is coanalytic complete;

  2. the family of all continua in In, n > 1 (n > 2), which contain no copy of a given nondegenerate chainable (circularly chainable) continuum Y is coanalytic hard; if Y is an arc (a simple closed curve), then the family is coanalytic complete;

  3. the set of all (strongly) countable-dimensional continua and the set of all weakly infinite-dimensional continua in the Hilbert cube are coanalytic hard.

Date received: February 8, 2001

Copyright © 2001 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 # cagh-61.