New posts in continuity

How to solve $\dot{x} = \frac{f(x)}{\|f(x)\|}$?

real-analysis ordinary-differential-equations dynamical-systems continuity gradient-flows

A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism

general-topology continuity compactness separation-axioms

Is there a function having a limit at every point while being nowhere continuous?

calculus real-analysis analysis limits continuity

The definition of continuously differentiable functions

real-analysis derivatives continuity definition

How to prove differentiability implies continuity with $\epsilon-\delta$ definition?

calculus real-analysis analysis derivatives continuity

How is the epsilon-delta definition of continuity equivalent to the following statement?

general-topology metric-spaces continuity definition epsilon-delta

$f$ brings convergent nets to convergent nets, is it continuous?

general-topology continuity nets

Is a function differentiable if it has a removable discontinuity

calculus derivatives continuity

How can a function with a hole (removable discontinuity) equal a function with no hole?

calculus limits continuity faq

Proving the inverse of a continuous function is also continuous

real-analysis metric-spaces continuity compactness inverse

$f:[a,b]\to \mathbb R$ is continuous iff graph of $f$ is connected and closed. [duplicate]

real-analysis continuity problem-solving

Additivity + Measurability $\implies$ Continuity

measure-theory continuity functional-equations

Is there a bijective seacucumber?

real-analysis continuity examples-counterexamples functional-equations

Does there exist a space filling curve which sends every convex set to a convex set?

real-analysis general-topology continuity convex-analysis

Assume $f\left({\frac{f(x)}{x}}\right)= f(x)$. Show that $ f$ continuous

real-analysis integration continuity

Equicontinuity on a compact metric space turns pointwise to uniform convergence

real-analysis general-topology functional-analysis convergence-divergence continuity

Is handoff / continuity (iOS 8+) supported in iTunes to seamlessly switch playback between Mac and iOS?

itunes continuity ios

How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.

calculus analysis continuity power-series functional-equations

If a function is undefined at a point, is it also discontinuous at that point?

real-analysis functions continuity

If $x$ is a càdlàg function and $f$ has compact support, how can we approximate $\sum_{s\in(a,\:b]}f(\Delta x(t))$?

real-analysis sequences-and-series functional-analysis continuity stochastic-analysis