New posts in continuity

Continuous function that take irrationals to rationals and vice-versa. [duplicate]

real-analysis functions continuity

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

sequences-and-series analysis continuity proof-verification uniform-continuity

The continuity of the expectation of a continuous stochastic procees

probability stochastic-processes continuity expectation

Constructing a strictly increasing function with zero derivatives

measure-theory continuity

How to show that $x^{1/n}$ is uniformly continuous

real-analysis continuity proof-explanation uniform-continuity

pointwise limit on a complete metric space

general-topology functional-analysis metric-spaces continuity

Are "locally continuous" functions continuous?

general-topology continuity

How to remove my Mac from iPhone call audio routing list?

macos ios audio call continuity

Dini's continuity vs Holder continuity

analysis continuity examples-counterexamples holder-spaces

Does continuity of $f$ imply $f^{-1}(\bar A)\subset\overline{f^{-1}(A)}$?

general-topology metric-spaces proof-writing continuity examples-counterexamples

f(x,y) not Differentiable on (0,0)

real-analysis limits analysis derivatives continuity

$f$ continuous on $(a,b)$ and $|f|$ differentiable on $(a,b)$; is $f$ differentiable in $(a,b)$?

real-analysis derivatives continuity

Distance of a point to a subset.

metric-spaces continuity compactness

iCloud Services (iMessages/FaceTime/Continuity) Very Broken on my Mac

macos icloud messages facetime continuity

Shouldn't this function be discontinuous everywhere?

limits continuity

Does continuity always imply integrability?

real-analysis integration continuity

How is the discrete metric continuous?

real-analysis continuity metric-spaces

Lipschitz continuity of $f(x) \to x^2$

continuity

$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$

real-analysis continuity holder-spaces

Handoff and Instant Hotspot with El Capitan on MacBook Pro (Retina, 15-inch, Early 2013)?

macbook-pro iphone macos continuity