Show that $[a,b] \cup [c,d]=T$, where $a < b$, $c < d$ and $b < c$ is not connected (subset of R)
In most books (as Rudin) there are propositions that uses the fact there exists $b < x < c$ and creates $(- \infty, x)\cap T$ and $(x ,+ \infty)\cap T$. Why are those intervals open? This must be open in R or $T$?
Thanks in advance!