It is very helpful to have all the assumptions of the main theorem written there explicitly, but is very explicit to refer to another place in the text.
Supposing A, B and C are Euclidean domains satisfying the conditions in assumption 3, then any topology that includes them is plain weird (see definition 2).
Here, assumption 3 is essentially a definition; mathematically, it would be the same to define a new concept which applies to triples (A, B, C).
If appropriate, you can use a qualifier like "technical/regularity/topological assumptions", which could make the theorem itself more informative.
This is especially relevant if there are several distinct sets of assumptions you need your object to satisfy.
Another approach would be to not give the entire theorem in the introduction, but rather give an interesting corollary or an elegant example, if any such exist, and refer the reader to the full theorem later in the paper.