encloses x" and is also topological in nature. A consequence of C1-2 is that E is reflexive and transitive, and hence a preorder. If E is also assumed extensional, so that: then E can be proved antisymmetric and thus becomes a partial order. Enclosure, notated xKy, is the single primitive relation of the theories in Whitehead (1919, 1920), the starting point of mereotopology. Let parthood be the defining primitive binary relation of the underlying mereology, and let the atomic formula Pxy denote that "x is part of y". We assume that P is a partial order. Call the resulting minimalist mereological theory M. If x is part of y, we postulate that y encloses x: C3. C3 nicely connects mereological parthood to topological enclosure. Let O, the binary relation of mereological overlap, be defined as: Let Oxy denote that "x and y overlap." With O in hand, a consequence of C3 is: Note that the converse does not necessarily hold. While things that overlap are necessarily connected, connected things do not necessarily overlap. If this were not the case, topology would merely be a model of mereology (in which "overlap" is always either primitive or defined). Ground mereotopology (MT) is the theory consisting of primitive C and P, defined E and O, the axioms C1-3, and axioms assuring that P is a partial order. Replacing the M in MT with the standard extensional mereology GEM results in the theory GEMT. Let IPxy denote that "x is an internal part of y." IP is defined as: Let σx φ(x) denote the mereological sum (fusion) of all individuals in the domain satisfying φ(x). σ is a variable binding prefix operator. The axioms of GEM assure that this sum exists if φ(x) is a first-order formula. With σ and the relation IP in hand, we can define the interior of x, as the mereological sum of all interior parts z of x, or: df Two easy consequences of this definition are: where W is the universal individual, and C5. (Inclusion) The operator i has two more axiomatic properties: C6. (Idempotence) C7. where a×b is the mereological product of a and b, not defined when Oab is false. i distributes over product. It can now be seen that i is isomorphic to the interior operator of topology. Hence the dual of i, the topological closure operator c, can be defined in terms of i,