New posts in Continuity

Prove that $S = \{ f: [0,1]\rightarrow \mathbb{R} \ \text{continuous} : x\in\mathbb{Q}\implies f(x) \in \mathbb{Q}\}$ is. uncountable

Solve $\frac{x^3-4x^2-4x+16}{\sqrt{x^2-5x+4}}=0$

$\frac{\partial F}{\partial y}\neq0\implies$ continuous contour line? (Implicit Function Theorem)

$a_{n+1} = \sqrt{2 + a_n}$ Specific Theorem Needed

Can we prove that polynomial functions can always be split into bijective restrictions?

Eliminating all removable discontinuities

Does a function $f$ with the following property exist?

Structure of the Mapping Cylinder of a Continuous Function

Derivative Greater Than 0 Implies One-To-One Function In Neighborhood

Example of absolutely continuous function $f$ with $\sqrt{f}$ not absolutely continuous