A continuous function can't take each of its values exactly twice
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.
108997
Continuous functions that attain local extrema at every point
15487
Continuous function from a connected set?
12349
a construction of a continuous function from a normal space to [0,1]
11974
product of two non zero continuous function is zero
153798
Problem involving maximum and minimum of a continuous function
39406
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
103241
A function that is continuous at the origin but not differentiable there
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
154572
Continuity of a function at an isolated point
71487
Real Analysis: Continuity of a Composition Function
55679
Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
109732
Nowhere continuous function limit
96729
Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$
140531
Why continuum function isn't strictly increasing?
58816
Existence of a continuous function which does not achieve a maximum.
28413
Limit of a continuous function