New posts in continuity

$f^{-1}(U)$ is regular open set in $X$ for regular open set $U$ in $Y$, whenever $f$ is continuous.

general-topology continuity

If $f:\mathbb{R}^n \to \mathbb{R}^n$ is continuous with convex image, and locally 1-1, must it be globally 1-1?

calculus real-analysis general-topology continuity

Is handoff available for Safari with Yosemite and iOS8.02?

iphone ios macbook-pro continuity

Why continuity requires bluetooth?

macos ios continuity

Infinity-to-one function

general-topology continuity infinity spheres

Graph of a function homeomorphic to a space implies continuity of the map?

general-topology continuity

Continuity of rational functions between affine algebraic sets

algebraic-geometry continuity rational-functions

Let $f(x) = x^3-x^2–3x–1$ and $h(x)=\frac{f(x)}{g(x)}$ where $h(x)$ is a rational function such that

calculus continuity

Is any compact, path-connected subset of $\mathbb{R}^n$ the continuous image of $[0,1]$?

general-topology analysis continuity compactness connectedness

Are continuous maps "weaker" than other morphisms?

general-topology continuity category-theory group-isomorphism morphism

Why is $\int_{[0,1]} \frac{dw}{1-wz}$ is holomorphic in unit disc?

integration complex-analysis proof-verification continuity contour-integration

Check the differentiablity of $\theta :\mathbb R^2 \setminus\{(0,0)\}\to \mathbb R$

real-analysis multivariable-calculus derivatives continuity

Topologically, is there a definition of differentiability that is dependent on the underlying topology, similar to continuity?

real-analysis general-topology derivatives continuity differential-topology

Continuous homomorphisms of Lie groups are smooth

differential-geometry continuity lie-groups lie-algebras smooth-manifolds

If a function is not continuous then is it possible for bounded function in given range? [duplicate]

calculus functions derivatives continuity bounded-variation

Continuity at exactly one point

real-analysis general-topology continuity

Functional equation $f(px)+p=[f(x)]^2$

real-analysis functions continuity functional-equations nonlinear-analysis

Prove a twice differentiable fucntion can only have at most two zeros [duplicate]

ordinary-differential-equations derivatives continuity

How can a $C^1$-continuous surface have infinite curvature?

differential-geometry continuity curvature

$f$ is continuous $ \iff $ $f^{-1}$ is continuous?

real-analysis continuity inverse