I will be taking Calculus I soon, and I just want to make sure I understand some concepts correctly.
So far, reading my book for Calculus I, I've encountered the definition of continuity as being defined on a closed interval $[a,b]$. This means that it exists at every single point in the interval including the endpoints, (meaning, that it can be approached from $a^+$, from $a^-$, from $b^+$, and from $b^-$, i.e., from both sides), correct? A polynomial would be such an example.
I looked through my book but there is no definition of continuity on an open interval $(a,b)$. Continuity on an open interval just means that it's approachable from only one side, either $a^-$ or $a^+$, or $b^+$ or $b^-$, but not only one of those, correct?
Is such a property the same thing as a one-sided limit? So, for example, ln would be an example of such a continuous property, since it's only defined for the positive numbers and thus can only be approached from one side?
So, then, does that mean that only a continuous function on a closed interval $[a,b]$ can attain a maximum/minimum value? A closed-open interval would also attain a maximum or a minimum but not both, such as $[a,b)$, correct?
sorry if these are too elementary for this website...