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A disturbing trend is putting adjectives as redirects on pages whose titles are noun phrases including those adjectives. This catches some badly formed links, but it also catches badly formed links that were never supposed to go there in the first place! I’m thinking of making a bunch of disambiguation pages whose page titles are adjectives just to put a stop to this.
So far, however, I’ve only created connective; and nothing links to it now, because I made all of the erstwhile links there link to noun phrases instead.
An alternative is to put the link to the most general form with that adjective; for example, I moved the redirect connected from locally n-connected (n,1)-topos (which isn’t actually about merely connected things except as a special case) to connected object (which does seem to be the most general article on connected things … so far).
A disturbing trend
Sorry if its me who is responsible for (parts of?) this trend. I came to like typing, say, -truncated as a convenient shorthand for the full title of the page that this links to. I am feeling that when typing I already have a vast amount of overhead with writing out the full links to -categorical entries.
to connected object (which does seem to be the most general article on connected things … so far).
Well n-connected object of an (infinity,1)-topos is also pretty general. However it assumes a little bit more than just an extensive category.
I don’t think that -connected things are more general than connected things; I’ve left n-connected as a redirect to n-connected object of an (infinity,1)-topos, but not connected. You can reduce overhead by writing [[n-connected]], although that doesn’t format the “n” correctly. (I might always come by later and change it to $n$-[[n-connected object|connected]] for you.)
I guess that I would encourage you to think whether the adjective has other meanings, which it may well have even when the full noun phrase does not. (That’s one thing that’s good about noun phrases as page titles.)
Oh, and you’re not the only one who links to adjectives; you may be the only one putting them in as redirects, but I don’t think so.
Another reason not to link to adjectives is if you really want to link to something more specific. What topologist, when writing [[connected]], really wants to go to connected object rather than to connected topological space? Better to play it safe and write [[connected space|connected]] from the beginning; you never know where that adjective is going to end up!
Agreed.
While we are at it: I find slightly troublesome the habit exhibited here and there on the Lab of writing “space” for “topological space”. There are so many other kinds of “space”s discussed on the Lab, that it seems wrong to assume that the default case is “topological space”. Accordingly, in the past I had renamed some entries that were titled “xyz space” to “xyz toplogical space”.
I would rather go the other way; keep the titles “xyz space”, but add to them details about about other kinds of spaces. I usually at least say something about locales if I can, when I see these.
If they only discuss topological spaces at first, that’s OK, but that would not be their ultimate purpose.
I agree with you, Tim.
On another thread, there has been mention of the horror ‘space = simplicial set’ and hence ’simplicial space = bisimplicial set’.
If the context is clear, that’s fine, but on the Lab where the context is wide, that is a bad habit in my opinion.
For instance: we are having this long discussion of good and proper simplicial topological spaces at nice simplicial topological space and geometric realization of simplicial topological spaces. Notice that if you identify “space” with “simplicial set” then these notions become empty. Then every simplicial topologial space is proper! (As discussed there.)
The trouble is really that you are violating a basic fact about category theory by conflating terminology like this: namely that it is not the objects that matter, but the category that they are objects of. Due to this there is a big difference between “topological space” as an object in the 1-category whose morphisms are continuous maps, and “topological space” in the -category/homotopy category of that, which is what you invoke by identifying it implicitly with a simplicial set.
Okay, I guess we all agree then.
I am for accepting a simplicial set as a kind of space, and I’m against interpreting “space” in general to mean topological space. However, I’m certainly also against interpreting “space” in general to mean simplicial set. (Other kinds of spaces that I know: -groupoids, Kan complexes, locales, objects in ASD, convergence spaces; topological spaces are, almost or exactly, special cases of all of these.) Both interpretations are OK in context, and page names with “space” are OK too, but those pages should cover the most general interpretation (even if they begin with topological spaces as the motivating case, and possibly the only case at first).
I’m not sure if this disagrees with the second paragraph of Tim #7, but otherwise I don’t think that it disagrees with anybody now.
It don’t disagree with me. My #7 is a statement of fact. When typing I often forget to put in precision of what type of space is being considered as my default tends to be a ’topological’ one. For me, I would not call an -groupoid a space. Rather it is a model of a space or homotopy type. I have got lost when articles refer to a homotopy type as a space, since they seem to me to be different concepts. Locales are almost spaces for me, but not quite… .
I would not like to be precise about what I do and do not mean by space. I have written papers with that as one of their themes. Perhaps, and that was a theme of the papers, we should almost have some idea of a ’presentation’ of a space, e.g., if someone has a possible (topological) space of solutions of some problem/equation whatever, and has a finite set of observations of solutions then they are giving a partial specification of the space but it may be the only thing we have to go on when working out what the characteristics of the space are. That leads to persistent homology, topological data analysis etc. and seems to be great fun. Perhaps a space is the abstraction we try to grab and all the things you mention are our attempts at encoding the ’spatial’ information about it. In any case, my point in #7 was to support the use of ’(adjective) space’ for at least the first use of a specific type of ’space’ in an entry, and to admit to bad practice.
OK, I agree with you that all of these things can be thought of as ways to present the underlying topological idea of what a space is. And the standard notion of ‘topological space’ is no exception; while it’s caught on as a formal standard in general topology (hence its name), it’s just one more way to present the underlying idea of a space.
Briefly taking up that theme, I think that a useful direction for someone’s research (possibly mine :-)) is to find translations between different notions of presentation of space. I like finite topological spaces, for instance, because they are neatly represented but although theoretically possible, the process of translating from a finite specification of a finite space to an intuition based on homotopy groups, -groupoids, etc. tends to be tedious and to go via other models. Then to go from a (finite) space to a (finite) locale then to a (finite) quantale to what…. . and that is just one of the directions possible. Fun!
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