Assume that Y is compact. Prove that f is continuous.
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
105700
Proving $\,f$ is constant.
145368
How to show $f:Y\to X^{+}$ is continuous?
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
130023
Prove that the sum of two continuous functions is continuous
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
129716
Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
55749
Compactly supported continuous function is uniformly continuous
40297
Proof of uniform limit of Continuous Functions
57180
Techniques to prove a function is uniformly continuous
54729
Prove that $f$ has a fixed point .
110146
I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
85623
Proof of continuity implied by differentiability