New posts in continuity

Proof of continuity of Thomae Function at irrationals.

Why not include as a requirement that all functions must be continuous to be differentiable?

Why did mathematicians introduce the concept of uniform continuity?

A continuous, nowhere differentiable but invertible function?

Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$

Theorem 18.1 of Munkres’ Topology

Continuity of the function $x\mapsto d(x,A)$ on a metric space

Is $f(x) = 1/x$ over $[0.1 , 1]$ uniformly continuous but $1/x$ on $(0,1)$ is not?

Proof of "every convex function is continuous"

Show that a continuous function has a fixed point

Continuity and the Axiom of Choice

Counter example restriction of a function

No continuous function switches $\mathbb{Q}$ and the irrationals

What functions can be made continuous by "mixing up their domain"?

Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?

A map is continuous if and only if for every set, the image of closure is contained in the closure of image

How to show that $f(x)=x^2$ is continuous at $x=1$? [closed]

A Topology such that the continuous functions are exactly the polynomials