Connected; touching; abutting.
Connecting without a break.
“the forty-eight contiguous states”
Without stopping; without a break, cessation, or interruption
“a continuous current of electricity”
Without intervening space; continued
“a continuous line of railroad”
Not deviating or varying from uniformity; not interrupted; not joined or articulated.
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.
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.”
Expressing an ongoing action or state.