ABSTRACT

The notion of connectedness corresponds roughly to the everyday idea of being in one piece. One condition when we intuitively think a space to be all in one piece is if it does not have disjoint \parts." Another condition when we would like to call a space one piece is that one can move in the space from any one point to any other point. These simple ideas have had important consequences in topology and its applications to analysis and geometry. In this section, we make the former intuitive notion precise and establish the basic properties of this concept. The formulation of the other intuitive notion will be considered in an other section.