Single point function is not a continuous function according to the intermediate value theorem
15690
Is a function defined at a single point continuous?
17234
Show that a continuous function has a fixed point
91482
Is there a short proof for the Intermediate Value Theorem
120947
continuous real-valued function
88240
Two functions discontinuous, but sum continuous
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
133696
Example of a function continuous at only one point.
38417
How to find the non-differentiable point(s) of a given continuous function?
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
131992
A problem on continuous functions
143174
property of continuous function
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
12240
Problem with a continuous function
71487
Real Analysis: Continuity of a Composition Function
101701
Prove that $\ln x$ is not uniformly continuous on $(0,1]$
118048
Can a function with just one point in its domain be continuous?