continuous

adjective6

1. •
   Without stopping; without a break, cessation, or interruption.

   • he can hear its continuous murmur — 1847
2. •
   Without intervening space; continued.

   • The dynamic tests at Wildenrath use continuous test tracks built on the site of a former Royal Air Force station that was vacated after the end of the Cold War. — 2023
3. •
   Not deviating or varying from uniformity; not interrupted; not joined or articulated.
4. •
   Expressing an ongoing action or state.
5. •
   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.
6. •
   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.