New posts in uniform-convergence

Consider $g_n(x)= \sqrt{x^2+1/n}$ for $x \in [-1,1]$ and $n$ be a natural number. Find the limit $g(x)$ of $g_n(x)$. Is the convergence uniform? [duplicate]

Compare the topology of pointwise convergence with the vector topology in the space of the continuous scalar functions $C(I)$

The sequence $n\sin(\sqrt{4\pi^2n^2 +x^2})$ converges on compacts:

Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence

the space of continuous functions is complete

If $|h(x,t)|\leq g(t)$ then the integral $f(x) = \int_a^{\infty} h(x,t)dt$ is uniformly convergent.

Dini's Theorem. Uniform convergence and Bolzano Weierstrass.

Theorems similar to Dini's Theorem and Egoroff's Theorem

Show uniform convergence of bounded functions implies uniform boundness.

Uniform convergence of a parametric integral. Which solution is correct?

$f_n$ uniformly converge to $f$ and $g_n$ uniformly converge to $g$ then $f_n \cdot g_n$ uniformly converge to $f\cdot g$

Is there integrable function sequence which is uniformly converges to not integrable function?

Examine the uniform convergence of $\sum_{n=1}^{\infty} \frac{x}{(1+nx)(1+(n+1)x)}$

Uniform Convergence of $\langle f_n \rangle = (nx)/(1+n^3x^2)$ for $0 \leq x \leq 1$

is uniform convergent sequence leads to bounded function?

Uniform limit of uniformly continuous functions

Uniform convergence and weak convergence

Exponential function and uniform convergence of polynomials.

Is a power series uniformly convergent in its interval of convergence?

$\sum_{n=1}^\infty\frac{z^n}{n}$ does not converge uniformly on $\mathbb{D}$.