Non-Complemented Open Sets in Effective Topology

Notions of effective complementation in effective topological spaces are considered, and several types of non-complemented sets are constructed. While there are parallels with recursively enumerable sets, some unexpected differences appear. Finally, a pair of splitting theorems is proved. 1980 Mathematics subject classification (Amer. Math. Soc): 03 D 45, 54 A 05.