I am reading "Topology 2nd Edition" by James R. Munkres.
There is the following sentence on p.90 in this book:
Now let $X$ be an ordered set in the order topology, and let $Y$ be a subset of $X$.
I am very poor at English.
What is the meaning of the following sentence?:
$X$ is an ordered set in the order topology.
Does the above sentence mean the following?:
$X$ is an ordered set and the topology on $X$ is the order topology.