New posts in continuity

Showing continuity of partially defined map

general-topology continuity homotopy-theory

I need the expression of a function which goes to infinity as x goes to 0 and has a finite integral

integration functions convergence-divergence continuity

$f:[0,1]\to[0,1]$ be a continuous function. Let $x_1\in[0,1]$ and define $x_{n+1}={\sum_{i=1}^n f(x_i)\over n}$.Prove, $\{x_n\}$ is convergent

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

Prove that if $f: \mathbb{R} \to \mathbb{Q}$ is continuous then $f$ is constant

real-analysis continuity

Method for proving continuity for a complex function

complex-analysis limits continuity

Gluing Lemma for Closed Sets: Infinite Cover Counter-Example

general-topology continuity examples-counterexamples

How do I prove this statement about winding numbers and continuous maps?

continuity winding-number

Theorem 10.2 Rudin

abstract-algebra integration analysis continuity

Functions from the Cantor set

real-analysis continuity cantor-set

To find continuous functions on $\mathbb R$ which preserve certain algebraic structures

real-analysis linear-algebra abstract-algebra continuity

A smooth nowhere analytic function such that all derivatives are monotone

real-analysis continuity examples-counterexamples analyticity monotone-functions

Show f is uniformly continuous on $(a,b)$ if it is continuous and $\lim\limits_{x\to a^+}f(x)$ and $\lim\limits_{x\to b^-}f(x)$ exist

real-analysis functions continuity

Continuity on closed intervals - differentiability on open intervals

Conditions for continuous extension of a function on an open set to its closure

real-analysis analysis continuity

Proof that a linear transformation is continuous

real-analysis proof-verification continuity

About uniformly continuity for bounded and continuous function

real-analysis analysis continuity uniform-continuity

If $|g(a)-g(b)| \leq |f(a)-f(b)|,$ for every $a,b$, and $f$ is a Darboux function, then $g$ is a Darboux function.

real-analysis continuity

Continuity of the inverse $f^{-1}$ at $f(x)$ when $f$ is bijective and continuous at $x$.

real-analysis continuity examples-counterexamples inverse

Extending continuous and uniformly continuous functions

real-analysis continuity

iOS 8 Handoff does not work between iPhone and iPad

iphone ipad wifi ios continuity