Almost continuous functions, two examples
by
Alejandro Illanes
Universidad Nacional Autónoma de México

An almost continuous function is a function f, between topological spaces X and Y, such that every open subset of the product of X and Y containing the graph of f, also contains the graph of a continuous function. Answering respective questions by F. Jordan and J. J. Charatonik, in this talk we present two examples.

1. A space X which is an almost continuous image of the real line such that X does not contain a dense arc component.

2. An almost continuous function from the unit interval into itself such that the induced function defined on the hyperspace of subcontinua of [0, 1] is not almost continuous.

Some other results and questions will be presented.

Date received: February 28, 2003