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We generalize the concept of combinatorial nested set complexes to posets andexhibit the topological relationship between the arising nested set complexesand the order complex of the underlying poset. In particular, a sufficientcondition is given so that this relationship is actually a subdivision. We usethe results to generalize the proof method of \v{C}uki\'c and Delucchi, so farrestricted to semilattices, for a result of Bj\"orner, Paffenholz, Sj\"ostrandand Ziegler on the Bier construction on posets.

Nested set complexes for posets and the Bier construction