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No. Closure is the property of a set with respect to an operation. You cannot have closure without a defined set and you cannot have closure without a defined operation.
It is called the property of "closure".
The closure property is an attribute of a set with respect to a binary operation, not only a binary operation. A set S is closed with respect to multiplication if, for any two elements, x and y, belonging to S, x*y also belongs to S.
Yes it has closure, identity, inverse, and an associative property.
The main difference between Kaleen closure and positive closure is; the positive closure does not contains the null, but Kaleen closure can contain the null.