I recently posted this question on Math Stack Exchange, in which I asked for a published reference containing the proof of a certain fact. What I got instead was a very rough outline of a proof. I've posted bounties of 200 and 400 points and still not gotten an answer to the reference request.

At this point, I would like to ask if anybody on Math Overflow can point me to a source that contains either the required proof or something close to it.

Would this be considered an acceptable question here?

Thanks.

**Edit.** I've been asked for the sources of these definitions, and why the ones I gave were equivalent to the ones I read.

The source with a definition equivalent to (1) is *Enciklopedija elementarnoj matematiki, Tom 5*, which on p. 67 defines a *polyhedral solid* to be any set that can be divided into a finite collection of tetrahedra whose interiors do not overlap. This restriction is not essential, as the same source states that a finite union of polyhedral solids is a polyhedral solid. (And in any case, I think this isn't terribly difficult to prove.)

Definition (2), in essence, comes from *Elementarnaja Geometrija* by Pogorelov. A *solid* is defined on page 164 as the closure of an open set path-connected by polygonal lines (which is equivalent to the interior being connected). A *polyhedron* is defined as a solid whose boundary consists of a finite number of polygons. Polygons are apparently to be understood to mean convex polygonal plane regions here. Admittedly, I have changed this definition by eliminating the connectedness requirement and requiring the solid to be bounded. If there is to be any hope of the definition becoming equivalent to (1), these changes are necessary in order to exclude from consideration, for instance, the exterior of a tetrahedron or an infinite trihedral region, in which case the "polygons" bounding it are themselves unbounded.

What I am really interested in is any equivalence of (1) with a definition in the spirit of (2).

whichquestion are you now talking about? I'd agree that themathematicalquestion whether the two definitions are equivalent does not need much motivation and does not really need sources either (though giving them is a plus, in my opinion)..Howeveryou make a point of this mathematical question, not being the question you intend to ask. Indeed, this mathematical question seems to be answered already. Thus, in my mind the question you intend to ask here could use some motivation. $\endgroup$ – user9072 Jan 22 '16 at 19:34