Without stopping; without a break, cessation, or interruption.
Expressing an ongoing action or state.
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.
Without intervening space; continued.
Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).
Without faltering, continuous, steadfast.