Abstract. Generalizations of normality, called (weakly) (functionally) θ-normal spaces, are introduced and studied. This leads to decompositions of normality. It turns out that every paracompact space is θ-normal. Moreover, every Lindelof space as well as every almost compact space is weakly θ-normal. Preservation of θ-normality and its variants under mappings is studied. This in turn strengthens several known results pertaining to normality.
2000 Mathematics Subject Classification. 54D10, 54D15, 54D20, 54D30.
Key words and phrases. θ-closed set, θ-open set, θ-normal space, θ-regular space, almost compact space, θ-continuous function.