New posts in continuity

When can you interchange composition of a limit?

limits continuity

Is there a simple-ish function for modeling seasonal changes to day/night duration and height of the sun?

functions trigonometry continuity mathematical-modeling

Compact topological space with closed graph implies continuity

general-topology continuity compactness

Is some thing wrong with the epsilon-delta definition of limit??

limits continuity definition epsilon-delta

Which $f$ satisfy the equation $\,\,f(x)\,f(y)-f(x+y)=\sin x\,\sin y\,$?

calculus trigonometry continuity contest-math functional-equations

Is showing that $x_n \rightarrow x_0\Rightarrow f(x_n) \rightarrow f(x_0)$ for a single sequence enough to prove continuity?

real-analysis continuity

How to show that $f$ is a straight line if $f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2}$?

continuity functional-equations

$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous

real-analysis calculus limits continuity epsilon-delta

Ideal in a ring of continuous functions

abstract-algebra ring-theory continuity ideals maximal-and-prime-ideals

If $\,\lim_{n\to\infty}f(nx)\,$ exists, for all $x\in\mathbb R$, then so does $\,\lim_{x\to\infty}f(x)\,$

calculus real-analysis limits continuity

Can we recover a space from its continuous functions?

general-topology continuity inverse-problems

composition of two uniformly continuous functions.

real-analysis continuity uniform-continuity function-and-relation-composition

Does factor-wise continuity imply continuity?

general-topology continuity product-space

Uniformly continuous function on totally bounded subset of complete metric space

real-analysis continuity metric-spaces uniform-continuity complete-spaces

Prove continuity/discontinuity of the Popcorn Function (Thomae's Function).

real-analysis sequences-and-series continuity

Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$

real-analysis continuity uniform-continuity cauchy-sequences

Why is $\frac{d}{dx}\ln(x) = \frac1x$ when the domain of $\frac1x$ includes $(-\infty,0)$?

calculus functions derivatives continuity

Continuity of the inverse matrix function

matrices derivatives continuity inverse

Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$

real-analysis analysis continuity uniform-continuity

Why aren’t continuous functions defined the other way around?

general-topology continuity intuition