List questions from continuity | MathQa

How discontinuous can the limit function be?

Published on 12 Jan 2025 - 19:12

Weierstrass continuity vs sequential continuity

Published on 12 Jan 2025 - 8:28

Functions that change definition with the type of input

Published on 12 Jan 2025 - 8:28

Find the number a that makes $f(x)$ continuous everywhere?

Published on 12 Jan 2025 - 8:28

Let $f(x) = 1$ for rational numbers $x$, and $f(x)=0$ for irrational numbers. Show $f$ is discontinuous at every $x$ in $\mathbb{R}$

Published on 12 Jan 2025 - 8:28

Show that $T$ is not a homeomorphism

Published on 12 Jan 2025 - 8:28

Is Lipschitz "type" function Continuous?

Published on 12 Jan 2025 - 8:28

Continuity of the function $\mathbb{R}^k \to\mathbb{R}: x\mapsto \ln(1+ \lVert x \rVert)$

Published on 12 Jan 2025 - 8:28

Function continuity $(x^2 - 1)/( x - 1)$

Published on 12 Jan 2025 - 18:25

Between uniform and pointwise convergence

Published on 12 Jan 2025 - 8:28