New posts in continuity

If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?

real-analysis general-topology continuity

$f(x) = x$ when x is rational, $f(x) = 0$ when x is irrational. Find all points at which $f$ is continous.

real-analysis proof-verification continuity

Existence of a power series converging non-uniformly to a continuous function

convergence-divergence continuity power-series

Continuity of a vector function through continuity of its components

multivariable-calculus continuity

How can you find the continuous digits of $g(x)=3 \lfloor x \rfloor^3$?

calculus continuity ceiling-and-floor-functions

Continuity of a function in two variables

real-analysis multivariable-calculus continuity

About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$

real-analysis continuity irrational-numbers rational-numbers

The inverse image of dense set is dense and of a comeager set is comeager?.

general-topology continuity descriptive-set-theory baire-category

Show that $f(x)=1/ x$ is continuous at any $c\neq 0$

real-analysis continuity

Is this true that a continuous function in a right-closed interval is bounded on that interval?

limits continuity upper-lower-bounds

If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?

real-analysis limits continuity

Prove that $\exists c > 0$ such that $||f||_2 \le c ||T(f)||_{\infty}$

functional-analysis continuity normed-spaces

Nonpiecewise Function Defined at a Point but Not Continuous There

calculus limits functions continuity examples-counterexamples

Auto-Unlock on a manually Continuity-enabled Mac?

mac apple-watch continuity

$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$? [duplicate]

real-analysis continuity

How to prove this limit composition theorem?

real-analysis limits functions continuity

Eliminating all removable discontinuities

real-analysis calculus continuity

Compactly supported continuous function is uniformly continuous

analysis continuity compactness uniform-continuity

Proving convexity of a function whose Hessian is positive semidefinite over a convex set

derivatives optimization continuity convex-optimization

Closed set mapped to itself in a compact Hausdorff space

general-topology continuity compactness