K. Whittington, A GENERALIZATION OF 2-HOMOGENEOUS CONTINUA BEING LOCALLY CONNECTED, Proceedings of the American Mathematical Society, 126(10), 1998, pp. 3131-3132
An elementary proof is given that if each pair of points of a homogene
ous metric continuum can be mapped by a homeomorphism into an arbitrar
ily small connected set, then the continuum is locally connected.