Prove this function cannot be continuous
7358
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
109732
Nowhere continuous function limit
14994
Showing a function $f$ cannot be surjective
76607
Show that exists a continuous function in $E$ that is not bounded
118207
Prove that the product of two continuous functions is continuous
17234
Show that a continuous function has a fixed point
118048
Can a function with just one point in its domain be continuous?
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
155170
Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition
98772
Continuity of a function in $\mathbb{R}$
127538
Show $f(x)=x\ln x$ is not uniformly continuous
58816
Existence of a continuous function which does not achieve a maximum.
99726
Proving that a function is not a contraction
145368
How to show $f:Y\to X^{+}$ is continuous?
60700
Continuity of a function to the integers
39235
Argue that the iterated integral of a continuous function is continuous