New posts in Order Topology

Can the long line be embedded in the ordered plane?

Open sets on ordered topology in $\mathbb{R\times R}$

Why are ordered spaces normal? [collecting proofs]

Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$