subconnected

Definition

A Hausdorff topological space is said to be T_i-subconnected if its topology is weaker than a T_i connected topology.

Reference

M. G. Tkachenko, V. V. Tkachuk, V. V. Uspenskij and R. G. Wilson, In quest of weaker connected topologies, Comment. Math. Univ. Carolin. 37,4 (1996), 825–841.
http://www.nsc.ru/EMIS/journals/CMUC/pdf/cmuc9604/tkauswil.pdf