The definition of continuity refers to something occurring in an uninterrupted state, or on a steady and ongoing basis.(noun)
When you are always there for your child to listen to him and care for him every single day, this is an example of a situation where you give your child a sense of continuity.
See continuity in Webster's New World College Dictionary
noun pl. continuities
Origin: OFr continuite < L continuitas
See continuity in American Heritage Dictionary 4
noun pl. con·ti·nu·i·ties
Learn more about continuity