Concerning upper semi-continuous collections of continua

Abstract

A collection of continua is said to be an upper semi-continuous collection if for each element g of the collection G and each positive number e there exists a positive number d such that if x is any element of G at a lower distance! from g less than d then the upper distance of x from g is less than e. The element ^ of such a collection 67 is said to be a limit element of the subcollection K of G if for every positive number e there exists some element of K which is distinct from p and whose upper distance from p is less than e.