Support `notation` and `keywords` fields for spaces/properties?

[StevenClontz]

Decided not to veer https://github.com/pi-base/data/pull/657 off-topic.

Once upon a time I pushed for non-mathematical names for our spaces. Now I'm wondering if I had it backwards: as the pi-base goes deeper into the weeds, we're going to wind up with more examples that don't have names besides maybe "Example x.y.z". But usually there's some kind of notation that could be used to describe these. So maybe...

uid: S000101
notation: \omega^{\mathfrak c}
name: Continuum power of a countable discrete space
aliases:
  - Uncountable products of $Z^+$
keywords:
  - (any words that someone might reasonably use to find this space but didn't fit into notation/name/aliases)
counterexamples_id: 103 # (unused, probably should be deprecated anyway)
refs:
- doi: 10.1007/978-1-4612-6290-9
  name: Counterexamples in Topology

And then we start displaying something like

$\omega^{\mathfrak c}$ (Continuum power of a countable discrete space)

And maybe only one of notation or name is required, displaying

$\omega^{\mathfrak c}$

or

Continuum power of a countable discrete space

if the other is missing.

I'm also curious what @awswan and @lunar-starlight think over at the topos fork.

[prabau]

About the keywords attributes, often a space can be determined, or at least the list of possible choices can be greatly reduced, by the properties of the space. This is already available via the Explore search box. There could be cases where keywords beyond properties of a space become useful. But before implementing this, I think it would be better to have some concrete examples showing the need for that feature.

[StevenClontz]

I don't recall offhand the example, but there was some situation where a user was typing something that wasn't quite in one of our given aliases, but was reasonable. We may have even added an alias that was basically the same as another alias or the main name, but used that conjugation of the word so it'd show up in search.

[prabau]

Seems worth an item for the next zoom meeting

[prabau]

Along the same line, we can discuss the use of "convenience aliases" for use in the search box in Explore. These are not meant as real aliases as attested in the literature, but more a convenience when doing manual searches. Examples: "T3" for $T_3$, "CG1" for $k_1$-space, "WLC" for weakly locally compact, etc. Possibly worth moving these out of aliases and into something like abbreviations:?

[StevenClontz]

Yeah, I think this is all the same thing: strings that should trigger results in search, but don't need to be displayed on the site.

[prabau]

notation: seems slightly different, about a way to display things when something like {S101} is expanded in text?