Let $f:[0,a]\times[0,b]\rightarrow\mathbb{R}$ be a continuous function. Prove a version of Fubini's Theorem:
54266
Prove that $\int_a^b \left( \int_c^d f(x,y)dy\right) dx=\int_c^d \left( \int_a^b f(x,y)dx\right) dy$
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
61640
Prove c exists for f:[0,1] -> R
73594
Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
77944
Injective functions with intermediate-value property are continuous. Better proof?
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
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continuous function: preimage of closure of a set is closure of preimage
150554
proof that $f'$ is continuous at $a$
80872
Remark from baby Rudin about continuous function
12523
Supremum of a Continuous Function is Continuous
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$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
117502
Proving that a certain continuous function is surjective.