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Constitutionally equivalent groups that occur in a single molecule are classified on the basis of their topic relationships by comparing their environments. The proposed classification extends earlier suggestions of Mislow and Raban. The existence of homotopic groups (those indistinguishable under any conditions) is related to the symmetry properties (gyrosymmetry) of rigid as well as flexible finite moieties. Stereoheterotopic groups (those that are distinguishable but occur in constitutionally equivalent environments) may be associated with various steric elements which will be fully discussed in a second paper. Each of these elements, the center, the axis, the plane and the torsional element, is divided into four mutually exclusive classes: the chiral and achiral elements of stereoisomerism; the prochiral and proachiral elements of prostereoisomerism. Of these classes, only the various centers of stereoisomerism and of prostereoisomerism are discussed in this report. Some modifications in our earlier proposals for the naming of individual stereoheterotopic groups are introduced. The utility of these new and revised terminologies for biochemical discussions is indicated. [ABSTRACT FROM AUTHOR]