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.