One thing that I hate about Baby Rudin is that the author doesn’t name the theorems after mathematicians; instead, he uses numbers (3.37,4.15 , etc ), and I think it is easier to remember if he uses names.
Definition 7.14 If $X$ is a metric space, $\mathscr{C}(X) $ will denote the set of all complex-valued, continuous, bounded functions with domain $X$.
I want to ask, what is the name of $\mathscr{C}(X)$? Does it have a name like other spaces (Hilbert space, measure space, etc.) or not?
Another question is: Is $\mathscr{C}$ a 'C' or an 'L' or '$\varphi$' ?