New posts in continuity

If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing

real-analysis calculus derivatives continuity monotone-functions

If a separately continuous function $f : [0,1]^2 \to \mathbb{R}$ vanishes on a dense set, must it vanish on the whole set?

real-analysis analysis multivariable-calculus continuity

Proof verification: To show that a function is not Lebesgue integrable.

real-analysis measure-theory continuity lebesgue-integral lp-spaces

If $f:\mathbb{R}\to\mathbb{R}$ is continuous and $f(x)\neq x$ for all $x$, must it be true that $f(f(x))\neq x$ for all $x$?

real-analysis general-topology continuity functional-equations

If $c$ is a local extreme but not a strict local extreme of a continuous $f$, then does there exist $X$ such that $x \in X$ and $f(X)=f(x)$?

real-analysis continuity maxima-minima

Show that $g(x)=\int_{-\infty}^x f(t) \ dt$ is continuous.

real-analysis calculus measure-theory continuity

Is the total variation function uniform continuous or continuous?

real-analysis continuity bounded-variation

Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?

real-analysis general-topology continuity

Tracing a curve along itself - can the result have holes?

general-topology geometry continuity connectedness curves

Is product of two Darboux functions Darboux?

real-analysis continuity

Extending $f: (0,1]\mapsto\mathbb{R}$ to a continuous function from $[0,1]$ to $\mathbb R$

real-analysis continuity definition

Starting a call from MacBook - Your iPhone needs to use the same iCloud and Facetime

iphone macbook-pro continuity

Are locally metrizable topological spaces sequential?

general-topology continuity metric-spaces

Proving that $f(x,y) = \frac{xy^2}{x^2 + y^2}$ with $f(0,0)=0$ is a continuous function using epsilon-delta. [duplicate]

real-analysis multivariable-calculus continuity

$f(f(\sqrt{2}))=\sqrt{2}$ then f has a fixed point

calculus continuity

Discontinuous inverse function

continuity epsilon-delta inverse-function

Find a general control and then show that this could have been achieved at x2

linear-algebra matrices ordinary-differential-equations continuity control-theory

Is there a continuous function from $[0,1]$ to $\mathbb R$ that satisfies

real-analysis continuity

Continuity of $f(x) = \left(\frac{2x}{1+x^2},\frac{1-x^2}{1+x^2}\right)$

real-analysis general-topology continuity stereographic-projections

Is the plane minus a line segment homeomorphic with punctured plane?

general-topology metric-spaces continuity