Continuous on a set
I am trying to figure out what it means for a function to be continuous on a set. Everything I look up just gives me answers on continuity at a point. I guess I am confused as to what the difference is. Does it have anything to do with LHS and RHS limits?
Solution 1:
A function is continuous at a set if it is continuous at every point of it.
Ex: $f$ is continuous at $A$ if $f$ is continuous at every $a\in A$