New posts in Continuity

Why is it enough for $\lim\limits_{h \to 0} \vert f(x+h)-f(x)\vert = 0$ to show uniform continuity

How come the $\epsilon-\delta$ definition of continuity is preferred over the sequential definition of continuity?

If $K$ is compact and $(f_k)\subseteq C(K)$ is dense, then $x_n\to x$ in $K$ iff $f_k(x_n)\to f_k(x)$ for each $k$

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

How can I find the value of this [pathological] function?

Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function

Can we apply L'Hospital's rule where the derivative is not continuous?

Continuity at a point in terms of closure

Give an example of a function that is bounded and continuous on the interval [0, 1) but not uniformly continuous on this interval.

How can a function with a hole (removable discontinuity) equal a function with no hole?