proposed tweaks for GO-space def

[prabau]

I had initially phrased the first two definitions in term of a local base of open nbhds of a point as I was worried it was required. But it seems that a local base of order-convex nbhds (without requiring open) is good enough. Please check the section "Alternate characterizations" that I added to https://math.stackexchange.com/questions/4917398 to see if that makes sense.

So given that, I like your more concise phrasing. Approving this, and letting you merge.

[StevenClontz]

Ah, well, my definition of "local base" is a collection of open sets. :-) I'd use the term "neighborhood base" to describe what I think you're using "local base" to mean: for every neighborhood $N$ of the point $x$, there exists a neigrborhood $M$ of $x$ in the neighborhood base such that $M\subseteq N$. Fortunately, the point is moot here I think.

[prabau]

Yeah, different authors may use different terminology. "Local base" and "neighborhood base" are synonyms in wikipedia and in Encyclopedia of General Topology (Hart, Nagata, Vaughan eds.). Willard uses "neighborhood base" and does not use "local base". But all three mean what you said above (with nbhds not assumed to be open).