Preimage of continuous one-to-one function on connected domain is not continuous.
62817
Functions which are Continuous, but not Bicontinuous
20377
Example 4.21 in Baby Rudin: Why is the inverse of this function not continuous at this point?
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
123132
Counterexample for a non-measurable function?
39406
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
157347
continuity, discontinuity derivative and relation to being derivative but its partials are not continuous
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
88240
Two functions discontinuous, but sum continuous
131992
A problem on continuous functions
126759
Unbounded continuous function on non-compact metric space
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
91682
Graph of a continuous function is closed
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
74145
How to prove $x^{n}$ is not uniformly continuous
140929
Increasing, continuous function implies connectivity and viceversa.
46834
show that a distance function is continuous
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?