Solving a Mereological Puzzle

There is an interesting puzzle about the interaction between mereology, topology, and dependence. It is not only interesting in and on itself, but also reveals subtleties about the aforementioned interaction that have gone unnoticed. The puzzle has it that the following plausible claims are jointly inconsistent: (i) wholes depend on their parts; (ii) boundaries are parts; (iii) boundaries depend on the whole they are part of. In the paper, I first argue that claims (i)–(iii) are not as a matter of fact inconsitent insofar as further assumptions are needed to get the puzzle off the ground. I consider several such assumptions, some more plausible than others. Though I do not take any definite stance as to whether the plusibility of the assumptions considered trump that of claims (i)–(iii), I set forth a suggestion to replace (iii) with something similar yet interestingly different.