The Lollipop Lemma and its uses
by
John C. Mayer
University of Alabama at Birmingham (UAB)
Coauthors: Harold Bell (University of Cincinnati), Lex G. Oversteegen (UAB), Edward D. Tymchatyn (University of Saskatchewan)

Bell's Lollipop Lemma is used to locate arcs of negative variation on a curve of index zero around a plane continuum admitting a fixed point free map. It can be used to show that any minimal counterexample to the fixed point property for non-separating plane continua (should one exist) must have exactly one geometric outchannel, necessarily of variation -1, under any continuous extension of the map to the plane.

Date received: February 9, 2001