Newbetuts

Prob. 23, Chap. 4 in Baby Rudin: Every convex function is continuous and every increasing convex function of a convex function is convex

The distance function on a metric space

For which conditions on countable sets does continuity implies uniform continuity

Prob. 11, Chap. 4 in Baby Rudin: uniformly continuous extension from a dense subset to the entire space

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

How to show that $x^{1/n}$ is uniformly continuous

If $p$ is a non-zero real polynomial then the map $x\mapsto \frac{1}{p(x)}$ is uniformly continuous over $\mathbb{R}$

A uniformly continuous function whose integral $\int_0^\infty f(x)dx$ exists converges to zero

Is a continuous function locally uniformly continuous?

An example of a bounded, continuous function on $(0,1)$ that is not uniformly continuous

If $f'$ is bounded, then $f$ is uniformly continuous

Checking uniform continuity of functions defined on the interval $(0, \infty)$

What's the difference between uniformly equicontinuous and uniformly continuous?

If every real valued continuous function on $X$ is uniformly continuous , then is every continuous function to any metric space uniformly continuous?

Is there a counter example for this statement?

Techniques to prove a function is uniformly continuous

About uniformly continuity for bounded and continuous function

New posts in uniform-continuity

$f$ is uniformly continuity

Characterisation of uniformly continuous function

Is uniform continuity related to the rate of change of the function?

Prob. 23, Chap. 4 in Baby Rudin: Every convex function is continuous and every increasing convex function of a convex function is convex

The distance function on a metric space

For which conditions on countable sets does continuity implies uniform continuity

Prob. 11, Chap. 4 in Baby Rudin: uniformly continuous extension from a dense subset to the entire space

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

How to show that $x^{1/n}$ is uniformly continuous

If $p$ is a non-zero real polynomial then the map $x\mapsto \frac{1}{p(x)}$ is uniformly continuous over $\mathbb{R}$

A uniformly continuous function whose integral $\int_0^\infty f(x)dx$ exists converges to zero

Is a continuous function locally uniformly continuous?

An example of a bounded, continuous function on $(0,1)$ that is not uniformly continuous

If $f'$ is bounded, then $f$ is uniformly continuous

Checking uniform continuity of functions defined on the interval $(0, \infty)$

What's the difference between uniformly equicontinuous and uniformly continuous?

If every real valued continuous function on $X$ is uniformly continuous , then is every continuous function to any metric space uniformly continuous?

Is there a counter example for this statement?

Techniques to prove a function is uniformly continuous

About uniformly continuity for bounded and continuous function