 Thus, any atomistic extensional mereology is truly “hyperextensional” in Goodman's (1958) sense: things built up from exactly the same atoms are identical. In particular, if the domain of an AEM-model has only finitely many atoms, the domain itself is bound to be finite. An interesting question, discussed at some length in the late 1960's (Yoes 1967, Eberle 1968, Schuldenfrei 1969) and taken up more recently by Simons (1987: 44f) and Engel and Yoes (1996), is whether there are atomless analogues of (27′). Is there any predicate that can play the role of ‘A’ in an atomless mereology? Such a predicate would identify the “base” (in the topological sense) of the system and would therefore enable mereology to cash out Goodman's hyperextensional intuitions even in the absence of atoms. The question is therefore significant especially from a nominalistic perspective, but it has deep ramifications also in other fields (e.g., in connection with a Whiteheadian conception of space according to which space itself contains no parts of lower dimensions such as points or boundary elements; see Forrest 1996a, Roeper 1997, and Cohn and Varzi 2003). In special cases there is no difficulty in providing a positive answer. For example, in the ÃEM model consisting of the open regular subsets of the real line, the open intervals with rational end points form a base in the relevant sense. It is unclear, however, whether a general answer can be given that applies to any sort of domain. If not, then the only option would appear to be an account where the notion of a “base” is relativized to entities of a given sort. In Simons's terminology, we could say that the ψ-ers form a base for the φ-ers if and only if the following variants of (P.5′) and (P.7) are satisfied: