Talk:Natural topology

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This article was created by accident. Many mathematics editors objected to its purpose or even existense. Here are excerpts from WT:WPM discussion.—Preceding unsigned comment added by Arcfrk (talk • contribs) 06:01, 26 June 2007 UTC

The full discussion can be found here. Although there was not agreement about whether this article should exist, there was some agreement at least that it should be linked with great caution! Geometry guy 09:53, 26 June 2007 (UTC)

[edit] Excerpts from discussion

A certain User:Karada has been linking every occurrence of the phrase natural topology to the non-existent article natural topology. I've reverted a few of them, but there are many more articles to go through. To the best of my knowledge, natural topology typically does not have a prescribed meaning (in the sense of natural transformation) although I can easily imagine some uses where the term is "natural" in the categorical sense. Since there is no article on the subject, is there a consensus here that these edits should be reverted? Silly rabbit 19:50, 24 June 2007 (UTC)

Another possibility is to write an article, such as natural (mathematics) covering the basic (imprecise) uses of the word natural in mathematics. I have no idea what such an article might look like, though. Thoughts? Volunteers? Silly rabbit 20:02, 24 June 2007 (UTC)

Thank you for your comments. "Natural topology" seems to be, at the very least, a mathematical jargon term, like "up to", with a specific meaning in topology, even if it does not have a precise formal meaning. If we can't explain what we mean by this, we are doing our readers a disservice. If it hasn't got a meaning which can be articulated, we shouldn't be using it at all. (…) -- Karada 20:17, 24 June 2007 (UTC)

I think it's usually a bad idea to write such articles, but if our hand is forced, then we have to be very upfront and clear about the fact that the term has no precise meaning (and hope no one asks for a citation, because hardly anyone bothers to note explicitly that terms with no precise meaning have no precise meaning). This is a very dangerous situation and can easily result in disaster articles like definable real number that can neither be easily fixed nor deleted. --Trovatore 20:27, 24 June 2007 (UTC)

It is a worthwhile term: the point is to make a particular map or collection of maps continuous. Often there is a "best" topology which does this. I've made a start. Please expand and add your own examples. Geometry guy 20:53, 24 June 2007 (UTC)

G-guy, I really think that was a bad idea. The problem with writing articles on imprecise terms is it tends to make them seem more precise than they are. You may think you've abstracted the commonality from the varied usages and made them genuinely precise, but that's original research. I think the best course of action now would be for you to request deletion of the new article -- if no one else has yet edited it, that can be done without further formalities. --Trovatore 20:56, 24 June 2007 (UTC)

How about simply adding a few sentences to Mathematical jargon instead of creating an article? Arcfrk 23:37, 24 June 2007 (UTC)

After checking out a few of these links to Natural topology, I came to the conclusion that such blanket linking a is really bad idea, since no matter what is at that page, it would not help understanding the meaning of the linked terms in the instances that I've reviewed (which is frequently subtly or completely different). Or to put it differently, there is no such an overriding thing as Natural topology as far as these linked articles are concerned. Arcfrk 00:49, 25 June 2007 (UTC)

My impression of the topic is that the meaning of "natural" is sociological or psychological: it has nothing to do with coarseness or making things continuous, it just means that there is one topology that most experts on the topic would pick as the most appropriate to use. I think that trying to nail the term down any further would be a mistake. The best we can hope for is a stubby article that says as much and points to a widely-varying collection of uses of "natural topology" in the literature to back up that point. But to do so would most likely be original research by synthesis. —David Eppstein 06:19, 25 June 2007 (UTC)

I'm glad you brought in original research by synthesis. That really brings the issue into focus for me. Linking natural topology to a particular use of the term would need to be cited, particularly for things like "the Zariski topology is natural" or "the Euclidean topology is natural". Both are true, but since neither is commonly introduced as a natural topology (in the strict sense), it would need to be referenced somehow. Silly rabbit 10:09, 25 June 2007 (UTC)