The equivalence of zero span and zero semispan

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 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 M is in class W W then the span of M M and the semispan of M M agree. These results are then applied to show that the properties of having zero span and of having zero semispan are equivalent.