Noun
(topology) A point of a connected space whose removal causes the resulting space to be disconnected.
Every point of a line is a cutpoint, but no point of a circle is a cutpoint.
(medicine) A cutoff point (cutoff value, threshold value), that is, a cutoff: the amount set by an operational definition as the transition point between states in a discretization or dichotomization.
Source: en.wiktionary.org