Hyperspace suspension and the fixed point property
by
Florencio Corona Vázquez
Facultad de Ciencias Físico Matemáticas - Benemérita Universidad Autónoma de Puebla
Coauthors: Raúl Escobedo

The hyperspace suspension of a continuum X, denoted by the symbol HS(X), is the quotient space C(X)/F₁(X), where C(X) is the hyperspace of subcontinua of X and F₁(X) is the space of singletons of X, topologized with the Hausdorff metric. A space X is said to have the fixed point property provided that every map f:X→ X has a fixed point, i.e., a point x ∈ X such that f(x)=x.

In this talk we give an example of a continuum X with the fixed point property such that HS(X) does not have the fixed point property (this answers a question posed by professor Nadler). We also present some fixed point results for hyperspace suspensions.

Date received: April 26, 2007