This paper is a study of Sum
Theorems for various classes of topological spaces. Specifically, suppose that X is a
topological space and {Fa} is a cover of X such that each Fα belongs to some
class Q of topological spaces. When can we assert that X is in Q? We shall
concentrate our attention on those cases where the elements of {Fα} are either
all open or all closed and the collection {Fα} is a σ-locally finite cover of
X.