E ectivity of Regular Spaces

General methods of investigating e ectivity on regular Hausdor (T3) spaces is considered. It is shown that there exists a functor from a category of T3 spaces into a category of domain representations. Using this functor one may look at the subcategory of e ective domain representations to get an e ectivity theory for T3 spaces. However, this approach seems to be beset by some problems. Instead, a new approach to introducing e ectivity to T3 spaces is given. The construction uses e ective retractions on e ective Scott{Ershov domains. The bene t of the approach is that the numbering of the basis and the numbering of the elements are derived at once.