Important statements could be marked to stand out more. (I have these in bold.)
[1] A poset which fulfills this is called a dcpo (directed-complete partial order).
[2] A continuous dcpo
There’s three paragraphs between [1] (where the term is defined) and [2] (where the term is first used outside of the definition). Now I understand why acronyms are usually IN ALL CAPS.
From now on, f;g;h will be a notation for “first apply f, then g, then h”. It’s the same as h∘g∘f, but without the need to take ten seconds to mentally reverse the order whenever it shows up.
This also seems to appears way before it’s used (below).
Specifically, our candidate for the embedding is: F(e,e′)(f)=p;f;e′, and our candidate for the projection going the other way is to map g:D′→E′ to e;g;p′. Let’s call this function P(e,e′) for later use. It’s a bit of work to show that these are continuous functions, so I’m gonna skip that part, but I will show the part about these two things fulfilling the relevant conditions for embeddings and projections.
Styling:
Important statements could be marked to stand out more. (I have these in bold.)
There’s three paragraphs between [1] (where the term is defined) and [2] (where the term is first used outside of the definition). Now I understand why acronyms are usually IN ALL CAPS.
This also seems to appears way before it’s used (below).