The Khalimsky topologies are precisely those simply connected topologies on Z<sup>n</sup> whose connected sets include all 2n-connected sets but no (3n-1)-disconnected sets.

T. Yung Kong The Khalimsky topologies are precisely those simply connected topologies on Z<sup>n</sup> whose connected sets include all 2n-connected sets but no (3n-1)-disconnected sets. 221-235 2003 305 Theor. Comput. Sci. 1-3 http://dx.doi.org/10.1016/S0304-3975(02)00710-7 db/journals/tcs/tcs305.html#Kong03