Size Maps and Size Levels in Hyperspace
by
Thelma West
University of Louisiana at Lafayette

Abstract Size Maps and Size Levels in Hyperspace Thelma West Let X be a continuum and let C(X) denote the hyperspace of subcontinua of X. A size map for C(X) is a continuous function µ: C(X)---> [0, +infinity) such that µ ({ x }) = 0 and if A is contained in B then µ (A)< or = to µ (B). This is in contrast to a Whitney map where the definition is the same except when A is contained in B and A not = B then µ (A) < µ (B). For example, the diameter map is a size map which is not in general a Whitney map. Point inverses of size maps are called size levels. Previously, size levels for arcs have been characterized. This characterization will be given and size levels for simple closed curves will be discussed.

Date received: April 14, 2000