A space X is n-weakly arcwise
connected (n-wac) if for every n points in X there is an arc connecting them,
while X is n-strongly arcwise connected (n-sac) if for every n points there
is an arc in X visiting them in order.

We will discuss various
characterizations of n-wac and n-sac in certain classes of continua. Then we
will apply ideas from descriptive set theory to see how good these
characterizations are...