A Class of Spaces Containing all Connected and all Locally Connected Spaces

A simultaneous generalization of connectedness and local connectedness, called sum connectedness, is introduced. The category of sum connected spaces forms the smallest co-reflective subcategory of TOP containing all connected spaces. A product theorem, analogous to that for locally connected spaces, is proved for sum connected spaces and a necessary and sufficient condition for the STONE -?ECH compactification of a TYCHONOFF space to be sum connected is obtained.