The equivalence of zero span and zero semispan

Davis, James Francis

doi:10.1090/S0002-9939-1984-0722431-3

The equivalence of zero span and zero semispan
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by James Francis Davis

Proc. Amer. Math. Soc. 90 (1984), 133-138

DOI: https://doi.org/10.1090/S0002-9939-1984-0722431-3

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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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