- Thread starter
- #1
The way you have written the statement makes it false.If $S\subseteq\mathbb{R}^n$, prove that $S$ is the union of all open subsets $\mathbb{R}^n$ which are contained in $S$.
This is described by saying that int $S$ is the largest open subset of $S$.
I don't really get this.
That is exactly how it is written in Apostles. Problem 3.10The way you have written the statement makes it false.
Do you mean that If $S$ is open then... ?
As written is is still false.That is exactly how it is written in Apostles. Problem 3.10
I just re-read it and I forgot the int.If $S\subseteq\mathbb{R}^n$, prove that the int $S$ is the union of all open subsets $\mathbb{R}^n$ which are contained in $S$.
This is described by saying that int $S$ is the largest open subset of $S$.
I don't really get this.
If $t\in\text{Int}(S)$ then there is an open set $O_t$ such that $t\in O_t~\&~O_t\subseteq S$.I just re-read it and I forgot the int.
I understand what you have written. How can int $S$ be the union of all open sets of $\mathbb{R}^n$. But $\mathbb{R}^n$ can be bigger than $S$.If $t\in\text{Int}(S)$ then there is an open set $O_t$ such that $t\in O_t~\&~O_t\subseteq S$.
Now finish it.
Where did Plato say that?I understand what you have written. How can int $S$ be the union of all open sets of $\mathbb{R}^n$. But $\mathbb{R}^n$ can be bigger than $S$.