# Are questions of the form "has this ever been studied?" appropriate?

Are requests of the form "has this ever been studied, and if so, may I please have a reference?" considered appropriate?

But let me be more specific.

So firstly, there's the point-set or "classical" approach to topology, which concerns itself with ordered pairs $(X,\tau)$ called topological spaces.

Then there's the pointless approach to topology, which concerns itself with lattices $(\tau,\wedge,\vee)$ called frames (in which finite meets distribute over arbitrary joins.)

I'm interested in a concept halfway between the two. We might call it "the classical approach, but with lattices." Rather than $(X,\tau)$, we concern ourselves $(P,\tau),$ where $P$ is a lattice that is isomorphic to a powerset lattice, and $\tau$ is a subset of $P$ that is closed with respect to arbitrary joins etc.

The motivation for this idea is as follows: we may be able to weaken the requirement that $P$ needs to be isomorphic to a powerset, and still be able to develop classical topology just fine.

So my question is, has this idea been studied before, and if so, may I please have reference recommended?

• One problem with this type of question is that they are semi-answerable: if the object has been studied, one can point to a reference, but there is no way to show that the subject has not been studied. It may have been studied, for example, and found to be useless so nothing was written as a result. Jan 28 '13 at 17:41
• @Mariano This comes to mind... ;-) Jan 28 '13 at 20:07
• @MichaelGreinecker, well, that is somewhat different. There can't be a standard notion of something for which one cannot give references! :-) Jan 28 '13 at 20:38
• Ask away, but now, ask it at math.stackexchange, the main site! Feb 1 '13 at 18:05

In my opinion, this kind of question is fine. I ask fellow mathematicians this kind of thing all the time and, when the answer is positive, it's very useful.

Questioners should understand, though, that if the true answer is "no" then the question will probably never be answered.

To add to David Speyer's answer, not only do I think such questions are fine, I think they are something in which (currently) sites like MathOverflow and Math.Stackexchange can excel (provided a positive answer exists).

Like David says, mathematicians ask each other these types of question all the time. And by their nature these are the types of questions where an intelligent expert can answer much better than a dumb search engine: if you only have a vague notion of something, it is hard for you to find the correct keywords to search for that something. Even doing a tree-search on Wikipedia will get you only so far.

That said, the usual "do your homework" part of asking a good question still applies: the more details your provide (what you have found out yourself, partial leads, motivation, etc.) the more likely that it will "click" with some other user giving you a good answer.

• I think this kind of site is one of the few places where you might get a negative response: "I'm in exactly that niche of that subfield and I've never heard of that; probably not studied." Not perfect, of course, but better than you'd get from asking around your department. Feb 5 '13 at 20:36