Span, surjective span, and chainability
by
Logan Hoehn
University of Toronto

The span of a metric continuum X is the supremum of the numbers inf{d(x, y): (x, y) ∈ Z} taken over all subcontinua Z of X² whose first and second coordinate projections are equal. Span was introduced by A. Lelek in 1964, and it has since been an open question whether a continuum has span zero if and only if it is chainable.

We will consider a slight variation of the above definition, also introduced by Lelek, called the surjective span. We will discuss some relationships and questions concerning span zero, surjective span zero, and chainability.

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Date received: February 19, 2009