Proving continuity of composition of continuous functions
71487
Real Analysis: Continuity of a Composition Function
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
125610
Space of bounded continuous functions is complete
126212
Proving uniform continuity on an interval
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions
100740
proof of that a continuous function has a fixed point
150554
proof that $f'$ is continuous at $a$
104044
Prove continuous functions $f$ and $g$ are equal
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
44574
Continuity of absolute value of a function
64487
Continuous function and dense set
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
146707
Formally show that the set of continuous functions is not measurable
111907
Prove that Cantor function is Hölder continuous