(set theory, order theory, of a binary relation R on a set X) The smallest binary relation on X that includes R and is transitive. / (set theory, of a set X) The smallest transitive set that contains X.

(algebra, field theory, of a field F) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).

(geology) The temperature, of a mineral, etc., below which there is no significant diffusion of isotopes into the external environment; the temperature of said mineral at the time it was formed (as calculated by radiometric dating).

plural of closure temperature

plural of Kleene closure

plural of deductive closure

Without closure.