Continua in which all connected subsets are arcwise connected

E. D. Tymchatyn
1975 Transactions of the American Mathematical Society  
Let X be a metric continuum such that every connected subset of X is arcwise connected. Some facts concerning the distribution of local cutpoints of X are obtained. These results are used to prove that X is a regular curve.
doi:10.1090/s0002-9947-1975-0365523-2 fatcat:dv5x6pqmynd53dvgz62cwo77tm