better first lines for properties with multiple characterizations

[StevenClontz]

Closes #1086

[prabau]

The suggestions seem ambiguous.

It used to be: Any of the following equivalent conditions: A, B, C, D.

Now: A, or any of the following equivalent conditions: B, C, D.
The meaning is: one of A, B, C, D. And B, C, D are equivalent. But A need not be equivalent to the other ones.

[prabau]

Compare with https://topology.pi-base.org/properties/P000135, which is more carefully worded.

[prabau]

I'll reiterate my comment from pi-base/web#177 (comment):

I think the most important thing is to have a clear and coherent text on each property page. What is displayed in the Properties list is not very important.

But I'll go along with this PR.

[GeoffreySangston]

Excluding the 'Any of the following equivalent properties holds:' examples, I think the following are all of properties with three or more definitions which contain "equivalent*", sorted by the way they're currently styled. Maybe we could decide on our favorite? I think we could change "Equivalently, any of the following equivalent properties holds:" to "This is equivalent to each of the following:".

1. ("Equivalently:")

• Simply connected P200
• Contractible P199
• Semimetrizable P102
• Has a point with a unique neighborhood P202
• Noetherian P208

2. ("Equivalently, any of the following equivalent properties holds:")

• T1 P2
• R0 P135

3. (Separate paragraphs per "Equivalently".. There's a lot more in this style with only two definitions.)

• Completely normal P14
• Countably compact P19
• Exhaustible by compacts P25
• Hereditarily collectionwise normal P108
• P-space P147
• GO-space P154
• k1-Hausdorff P170
• sigma-connected P189

4. (In-paragraph equivalents.. possibly because the following paragraph works well with it.)

• Perfectly normal P15

5. ("And alternatively")

• k2-Hausdorff P171

[prabau]

I think we could change "Equivalently, any of the following equivalent properties holds:" to "This is equivalent to each of the following:".

Yeah, that reads much better, and is also correct.

[GeoffreySangston]

I don't mind doing the tedious work of switching these all to one style. Probably not for a few days.

[prabau]

Hmm, what do you have in mind exactly? I think it's fine to change the introductory sentence when there is a list of bullet points. But in my opinion, we may not want/need to convert everything to bullet points.

I agree with splitting the paragraph for P15 (your category 4).

[GeoffreySangston]

1. Definitely merging styles 1 and 2 into a single agreed upon version. And fixing 5. (And I figured 4 also.)
2. Superseded possibly by switching everything to the style we thought was the best, yet to be determined. I guessed that would be bullet points, but I'm also happy not switching everything to one style if it's deemed too unimportant.

Maybe going forward we could agree on a favored style for new properties? I don't see why to prefer the separate paragraph style, because then following paragraphs aren't as easily distinguishable from equivalent definitions.

[prabau]

I don't see why to prefer the separate paragraph style, because then following paragraphs aren't as easily distinguishable from equivalent definitions.

We'll have to play it by ear. I vaguely remember there were some cases of definitions involving multiple paragraphs, followed by some equivalent other characterizations in still other paragraphs. Forcing a bunch of paragraphs to be scrunched together in a single bullet does not seem optimal.

But overall, to me it does not seem very important if we don't have a uniform style for this. The main thing is to have something clear and unambiguous. And I am ok with having the first line more descriptive of the property, if some people care about that.

Also note: for just two definitions, there is no sense in using bullets.

[GeoffreySangston]

Sorry Steven. Afterwards I realized this would have been the ideal place to test out the 'suggestion' feature. I'll do it next time!