And what is wrong with the word compactified? We have rectified, vilified, intensified. We have intensification and rectification. Compactification seems to me to be the ordinary and natural word for the process of rendering something compact.
There is, I suppose, a word 'compaction', but that has images of large dustcarts eating cardboard boxes: I'd prefer a new coinage, for clarity. Compaction might falsely give images of gravitational compaction, as in a neutron star: in fact it might even already be in use in that context, now that I think of it. Yes, neutron matter is compacted, topological spaces are compactified.*
As for verbs, we have both 'compact' and 'compactify'. Certainly, all other things being equal, it's a tenet of good usage to prefer the shorter word to the longer. But the existence of 'compactification' means that analogy weighs on the side of 'compactify'. And preference for short words is a very bad principle if it's made to outweigh all other considerations.
It's a natural formation, in accordance with English usage, whose structure is transparent, whose meaning is clear, which violates no logic, and presents no phonetic awkwardness. It is useful in its context, and makes it clearer. I can't see anything wrong with such words.
* Assuming the word does have any relation to the topological process of furnishing with a finite covering of open sets. I haven't heard of that in the context of string theory. It would be amusing if the word was just a journalist's error after all.
