continuous

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

a continuous current of electricity

he can hear its continuous murmur

Without intervening space; continued.

a continuous line of railroad

[…] the Plan incorporates in proper combination every available modern technique, including extensive electrification on the new standard high-voltage a.c. system at a frequency of 50 cycles; main-line diesel traction as a half-way house to electrification; lightweight diesel trains for secondary and branch services; and a smaller wagon fleet doing more work by the use of continuous brakes in conjunction with modernised terminals and marshalling yards.

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.