Definition of "continuity"

Vacuum-fitted wagons are provided with complete vacuum-brake equipment; "piped" wagons have through pipes, enabling them to be marshalled in vacuum-braked trains without interrupting the continuity of the vacuum brake connections, but are not provided themselves with vacuum brake gear.

1946 March and April, “The Why and The Wherefore: "Fitted" and "Piped" Wagons”, in Railway Magazine, page 128

As on Nos. 20001-3, the motor and generator armature shafts of the new locomotive each carry a heavy flywheel to provide kinetic energy and help maintain the speed of the motor-generator set during interruptions of supply, as at breaks in the continuity of the conductor rail.

1959 March, “The 2,500 h.p. electric locomotives for the Kent Coast electrification”, in Trains Illustrated, page 123

The definition of a continuous function assumes that the function is already defined for x = a. If this is not the case, however, it is sometimes possible to assign such a value to the function for x = a that the condition of continuity shall be satisfied.

1911, William Anthony Granville, Elements of the Differential and Integral Calculus

In “Treehouse Of Horror” episodes, the rules aren’t just different—they don’t even exist. If writers want Homer to kill Flanders or for a segment to end with a marriage between a woman and a giant ape, they can do so without worrying about continuity or consistency or fans griping that the gang is behaving out of character.

2012 April 29, Nathan Rabin, “TV: Review: THE SIMPSONS (CLASSIC): “Treehouse of Horror III” (season 4, episode 5; originally aired 10/29/1992)”, in (Please provide the book title or journal name)‎