Why can't $\psi' (x,t)$ be discontinuous?
18321
Smoothness constraint of wave function
40576
Intermediate value property problem and continuous function
114691
Why can't differentiability be generalized as nicely as continuity?
117419
Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
18511
Can we construct a function that has uncountable many jump discontinuities?
109732
Nowhere continuous function limit
109666
Example where partial derivatives commute but are not continuous.
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
118192
Is there a bijective function $f: \mathbb{R}\to\mathbb{R}$ that is discontinuous?
128719
Are constants the only continuous functions with "symmetric derivative" zero?
127114
Differentiability implying continuity
82280
Problem about continuous functions and the intermediate value theorem
140153
Conjectures Involving floor(x)/piecewise continuity with regards to Integration and Differential Equations
112404
Eliminating discontinuities for increasing function
131992
A problem on continuous functions
74684
$\lim_{x \to 0} {1-x\cot x\over x^2}$
39406
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?