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Shape morphisms and components of movable compacta

Published online by Cambridge University Press:  24 October 2008

José M. R. Sanjurjo
José M. R. Sanjurjo
Affiliation:
Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
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Extract

The relationship between components and movability for compacta (i.e. compact metric spaces) was described by Borsuk in [5]. Borsuk proved that if each component of a compactum X is movable, then so is X. More recently Segal and Spiez[19], motivated by results of Alonso Morón[1], have constructed a (non-compact) metric space X of small inductive dimension zero and such that X is non-movable. The construction of Segal and Spiez was based on the famous space of P. Roy [16]. On the other hand, K. Borsuk gave in [5] an example of a movable compactum with non-movable components. The structure of such compacta was studied by Oledzki in [15], where he obtained an interesting result stating that if X is a movable compactum then the set of movable components of X is dense in the space of components of X. Oledzki's result was later strengthened by Nowak[14], who proved that if all movable components of a movable compactum X are of deformation dimension at most n, then so are the non-movable components and the compactum X itself.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 481 - 486
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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