How to prove $X^{\omega}$ with a product toplogy is metrizable with $\rho(x,y) =\sum_{n=1}^{\infty}2^{-n}\frac{d(x_n,y_n)}{1+d(x_n,y_n)}$?
94438
Show that the countable product of metric spaces is metrizable
34918
Difference between $R^\infty$ and $R^\omega$
25498
Prove that $\omega + \omega_1 = \omega \cdot \omega_1 = \omega^{\omega_1} = \omega_1$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
61810
An application of Borel-Caratheodory theorem
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
140249
Euler Product formula for Riemann zeta function proof
41298
Understanding proof of completeness of $L^{\infty}$
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
20789
If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true?
156727
A step in the proof of Characterization of $W^{1,\infty}$
108837
How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
86193
Rigorous proof that $dx dy=r\ dr\ d\theta$
68320
Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$
10702
Show that $\left\{A\subset\Omega: A~\text{ is countable or }A^C\text{ is countable}\right\}$ is a $\sigma$-algebra
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?