On characterizing extendable connectivity functions by associated sets (Q1374591)

It is shown that the class of extendable connectivity functions from \([0,1]\) into \([0,1]\) cannot be characterized in terms of associated sets. The same remains true for the class of uniform limits of sequences of extendable connectivity functions. An example of an almost continuous function from \(R\) into \(R\) which is not the uniform limit of any sequence of extendable connectivity functions is given.