New posts in continuity

Is $\ln(x)$ uniformly continuous?

real-analysis analysis continuity uniform-continuity

A function is said to be continuous. Can it still have vertical asymptotes?

calculus limits continuity

Functions that are continuous only at two points?

real-analysis functions continuity

Can a cube of discontinuous function be continuous?

Converse of compactness

general-topology continuity compactness

Axiomatizing topology through continuous maps

general-topology continuity axioms

for every convergent sequence $x_n$, $f(x_n)$ also converges. Does this imply continuity of f?

sequences-and-series general-topology metric-spaces continuity

Condition for an additive function to be continuous

real-analysis continuity functional-equations

Riemann-stieltjes integral and the supremum of f

integration analysis continuity bounded-variation

Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line

real-analysis multivariable-calculus continuity

Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.

real-analysis continuity uniform-continuity

$f$ be a smooth function on real line , $f(0)=0$ , $f(x)>0, \forall x \ne 0$ and any $f^{(n)}(0)=0$ ; is $\sqrt f$ smooth?

real-analysis derivatives continuity

Why can a discontinuous function not be differentiable?

calculus functions continuity

Geometric intepretation of Holder continuous functions?

functional-analysis partial-differential-equations continuity holder-spaces

Example of a function differentiable in a point, but not continuous in a neighborhood of the point?

calculus derivatives continuity

Understanding the proof of $l_2$ being complete.

real-analysis sequences-and-series limits convergence-divergence continuity

Combination of continuous and discontinuous functions

functions continuity

Who gave you the epsilon?

calculus continuity math-history nonstandard-analysis infinitesimals

Does there exist a continuous $g(x,t)$ such that every continuous$ f(x)$ equals $g(x,t)$ for some $t$ and all $x$??

calculus multivariable-calculus continuity

Continuity of differentiable function $x^2\sin(1/x)$

functions derivatives continuity