I conjecture that if a function is continuous at a discreet point (say p), it is continuous at all points in some delta-neighborhood of p.
Am I correct? If yes - any pointers to prove this? If not - any counterexample.
For those who know the subject deeper - is this kind of formulation even important?
Thanks. But it sounds conter-intutive to me.
In layman's way, being continous at 'a' means 'very' close to 'a' value of the function varies 'very' little. So the same will apply to any point which is very very close to 'a' and thus I say it will be continous to at all points in some delta-neighbourhood of a.
I know I am talking an all vague language but it helps get a feel of definitons. Please excuse me if all this is not important/relevant.
Using the same method it can be show that this result also holds if .