Closure of $ell^2$ in the space of real sequences
Using the product topology on $overline{mathbb{R}}^omega$, is $ell^2$ (the space of real square summable sequences) a dense subset of $overline{mathbb{R}}^omega$ ?
Tag: general-topology
The boundary of a domain without a closed subset
Let $D$ be a bounded domain in $mathbb{R}^{N}$ ($Ngeq2$) and $E$ a closed subset of $D$ with empty interior. Show that the boundary of $Dsetminus E$ is the union of $E$ and the boundary of $D$: $$…
$mathbb{N}$ complete metric space
I’m trying to prove that $(mathbb{N},d)$ is a complete space where $d=left | m-n right |$. So I define $a_{n}:=n$ , if it’s cauchy we know that $forall epsilon$>0 there exist $Nin mathbb{N}$ s….