New posts in continuity

If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex [duplicate]

real-analysis analysis continuity convex-analysis functional-inequalities

Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.

real-analysis continuity uniform-continuity

What is the geometrical difference between continuity and uniform continuity?

real-analysis continuity uniform-continuity

Construct a monotone function which has countably many discontinuities

real-analysis functions continuity examples-counterexamples

Prove that the inverse image of an open set is open

real-analysis continuity

Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?

real-analysis continuity examples-counterexamples

A game with $\delta$, $\epsilon$ and uniform continuity.

real-analysis continuity solution-verification uniform-continuity

Can a nowhere continuous function have a connected graph?

general-topology connectedness continuity

Unusual Dock Icon Appearing in OS X 10.10 Yosemite

macos ios mac google-chrome continuity

Let $X,Y$ be Hausdorff and $f,g : X \to Y$ continuous. Let $A \subset X$ be dense and suppose that $f\mid_A = g\mid_A$. Show that $f=g$.

general-topology continuity solution-verification separation-axioms

The set of points where two maps agree is closed?

general-topology continuity separation-axioms

Differentiability implies continuity - A question about the proof

real-analysis derivatives proof-writing continuity

Continuity of $L^1$ functions with respect to translation

real-analysis measure-theory limits continuity lebesgue-integral

Why are removable discontinuities even discontinuities at all?

algebra-precalculus limits functions continuity

Real Analysis: Continuity of a Composition Function

real-analysis continuity function-and-relation-composition

Why are real numbers useful?

calculus real-analysis soft-question continuity real-numbers

How do I show that all continuous periodic functions are bounded and uniform continuous?

real-analysis continuity uniform-continuity periodic-functions

Show that max $|f(x)| ≥ (c_0/8) (b − a)^2$

real-analysis functions derivatives continuity taylor-expansion

How big is the set of Hölder continuous functions?

real-analysis analysis continuity holder-spaces

Is the distance function in a metric space (uniformly) continuous?

general-topology metric-spaces continuity uniform-continuity