A simplicial complex of dimension $d$ is called constructible if it is a simplex, or if it is the union of two constructible dimension-$d$ simplicial complexes along a dimension-$(d-1)$ intersection. Who first came up with this definition? I had thought it was M. Hochster [Ann. Math. 96 (1972), 318-337], but a number of sources cite E. Zeeman [Seminar on Combinatorial Topology, Fascicule 1, Expos\'es I \'a V inclus, Institut des Hautes Etudes Scientifiques, 1963]. I've looked at Zeeman's book and don't see where he considers this condition, even under a different name. Can anyone point to the appropriate part of Zeeman? (Disclosure: This is a referee's suggestion for a paper I am revising, and I would like to make the citation pinpoint if possible.)



Who first considered constructibility of simplicial complexes?
If you want the first use of the term "constructible" in this context, then your reference to Mel Hochster's work is right-on. But if you want the actual notion, then things get slightly hazy. I think the oldest (implicit) use is Newman's two papers from 1926 called something like The foundations of combinatorial analysis situs (not near my reference books, so the title might be off).


**Update** Although I remain parted from my books, I should thank Joe O'Rourke for locating the desired references, namely



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> Newman, Maxwell Herman Alexander. "On the foundations of combinatorial analysis situs." In Proc. Royal Acad. Amsterdam, vol. 29, pp. 610-641. 1926.
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And also, the OP might benefit from the introduction (paragraph 2) of [this paper](http://arxiv.org/abs/math/0309149)



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> Frank Lutz, *Small examples of non-constructible simplicial balls and spheres*,
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which supports both assertions: that Newman's work is the earliest where the idea of constructibility appears, predating Alexander by $\epsilon$; and also that Hochster's paper is the first place where it gets its present name.


