Is interval $(a, \infty]$ a Borel set ?
I hear that if $U$ is written as union, intersection, or subtraction of open sets, $U$ is called a Borel set.
I wonder whether $(a, \infty]$ is a Borel set or not.
$\cup_{n=1}^{\infty} (a, n]$ isn't equal to $(a, \infty]$, and I tried to write $(a, \infty]$ as union, intersection, or subtraction of open sets but I couldn't.
How can I write $(a, \infty]$, or isn't $(a, \infty]$ a Borel set ?
In which space are you working? If you are working in the extended real line with the order topology, then $(a, \infty]$ is open by definition of order topology, hence a Borel set.