Closed -> Closure, Open ->?
Am I right in assuming that the word closure is derived from the word closed?
If so, I would be interested to know the name of this procedure and what it yields when applied to the word open.
My motivation is a mathematical one: "The closure of a set is the smallest closed set containing it." For certain topological spaces (Alexandrov spaces) it is true that every set is contained in a smallest open set.
My maths isn't good enough for me to grasp exactly what the closure of a set actually means. In fact, I can't even tell whether it's meaningful to speak of an "opposite" in this context.
By way of example, in perspective drawing you can speak of a vanishing point, but I don't think anything could meaningfully be called an "appearing point", regardless of the actual term used.
At the more general linguistic level, closure is effectively an alternative noun to the more common closing, though it's obviously acquired specialised meanings in the contexts of mathematical set theory and psychology/counselling. I don't think there's a corresponding alternative form for the "opposite" noun opening.
Per my answer to this question, I call the process by which we create words such as closure from close linguistic production. I don't know if the -ure suffix is still "productive" (ie - can be used to make "new" word-forms). I suspect not, but maybe it is used for obscure new technical terms.
Not exactly. From EtymOnline
closure late 14c., "a barrier, a fence," from O.Fr. closure "enclosure; that which encloses, fastening, hedge, wall, fence," also closture "barrier, division; enclosure, hedge, fence, wall" (12c., Mod.Fr. clôture), from L. clausura "lock, fortress, a closing" (cf. It. chiusura), from pp. stem of claudere "to close" (see close (v.)). Sense of "act of closing, bringing to a close" is from early 15c. Sense of "tendency to create ordered and satisfying wholes" is 1924, from Gestalt psychology.
Although ultimately deriving from close, this word was not derived from it in English, but rather came directly from French. Whether it's some standard process or not is beyond my knowledge.