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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The equivalence of zero span and zero semispan


Author: James Francis Davis
Journal: Proc. Amer. Math. Soc. 90 (1984), 133-138
MSC: Primary 54F20; Secondary 54C10, 54F50, 54H25
MathSciNet review: 722431
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Abstract: In this paper we introduce the idea of the symmetric span of a continuum, and show that continua with zero symmetric span are in class $ W$. Continua with zero span have zero symmetric span, but the converse does not hold. We also show that if every subcontinuum of the continuum $ M$ is in class $ W$ then the span of $ M$ and the semispan of $ M$ agree. These results are then applied to show that the properties of having zero span and of having zero semispan are equivalent.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722431-3
PII: S 0002-9939(1984)0722431-3
Keywords: Span, semispan, weakly confluent mappings, fixed point property
Article copyright: © Copyright 1984 American Mathematical Society