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On hereditarily indecomposable compacta
by
Elzbieta Pol
University of Warsaw, Poland
Coauthors: Klaas Pieter Hart
We say that a compactum X is hereditarily indecomposable if for every two intersecting continua in X one is contained in the other.
We prove the following thorem. Let f be a perfect map with hereditarily indecomposable fibers from a separable metrizable space X onto a zero-dimensional separable metrizable space Y. Then there are a hereditarily indecomposable metrizable compactification X' of X with dimX'=dimX and a zero-dimensional metrizable compactification Y' of Y such that f can be extended to a map f' from X' onto Y'.
As a corollary we obtain a theorem of T.Mackowiak on the existence of universal n-dimensional hereditarily indecomposable continua.
Date received: February 4, 2009
Copyright © 2009 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 # caxy-36.