Continuing or continuous?

noun A continuation

adjective UKBeing the successor to a no longer extant organization, operating under the same name and usually claiming to be the same entity

adjective Without stopping; without a break, cessation, or interruption

the continuous roar of a waterfall

adjective Without intervening space; continued

a continuous line of railroad

adjective Not deviating or varying from uniformity; not interrupted; not joined or articulated

adjective Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D

adjective Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function)

Each continuous function from the real line to the rationals is constant, since the rationals are totally disconnected

adjective Expressing an ongoing action or state