CONCERNING THE EXTENSION OF CONNECTIVITY FUN(~TIONS

In his classic paper, Stallings [7] asked if a connec tivity function I ~ I could always be extended to a connec 2 2tivity function 1 ~ I when I is considered embedded in 1 as I x O. Several authors answered this negatively by giving examples of connectivity functions I ~ I which are not almost continuous, [1], [6].. In [7] Stallings proVed that an almost continuous function I ~ I is a connectivity function and, curiously enough, a connectivity function 21 ~ I is an almost continuous function. Later it was shown by Kellum [4] that an almost continuous function I ~ I can 2be extended to an almost continuous function 1 ~ I. This naturally leaves the question "can an almost continuous function I ~ I be extended to a connectivity function 1 2 ~ I? " Theorem 2 of this paper together with the first example of [2] shows that this is not the case