Thinking of a function that is continuous only at one point
133696
Example of a function continuous at only one point.
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
158567
A uniform continuous function which is not Hölder continuous
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
26955
Continuous at exactly two points and differentiable at exactly one of them
98772
Continuity of a function in $\mathbb{R}$
18082
A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
83338
Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
143174
property of continuous function
76396
Nowhere monotonic continuous function
131992
A problem on continuous functions
28392
Construct a monotone function which has countably many discontinuities
102075
A function continuous on all irrational points
62947
If $f(x)$ is equal to $x$ or $1-x$ when $x$ is rational/irrational, then $f$ is continuous only at $x=1/2$
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
44574
Continuity of absolute value of a function
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.