Talk:Evenly spaced integer topology

Just a signature[edit]

Mathematrucker (talk) 19:01, 6 July 2019 (UTC)[reply]

Removal of reference[edit]

I wish to contest the removal of the reference [1]. This was moved on the specious grounds that the reference failed to explicitly mention coarsest topologies and arithmetic progressions. As we all know, the topology generated by a set of subsets is, indeed, the coarsest topology (however one wants to state that: the smallest topology sounds a little odd to me, but is also very common.) This is not controversial knowledge in any way. As for the arithmetic progressions, the cited source says exactly this:

"The basis sets are simply cosets of subgroups of the integers."

That is, the basis sets are simply arithmetic progressions. It seems rather gratuitous to bring in subgroups and cosets when we have a more common term for this special case. Sławomir Biały (talk) 13:06, 5 October 2010 (UTC)[reply]

How can the sentance "The basis sets are simply cosets of subgroups of the integers" be used to justify that "The evenly spaced integer topology is the coarsest topology that includes as open subsets the family of all arithmetic progressions: that is, arithmetic progressions are a subbase (and, in fact, a base) for the topology"? I'm sorry but there's a lot of background work to be done to justufy that step, work which would violate wp:original research. You'll need to provide another source that verifies the claimed implication. — Fly by Night (talk) 13:13, 5 October 2010 (UTC)[reply]

P.S. You should be careful using phrases such as "as we all know". The article should be accessible to as many people as possible. It should be verifiable and it should not contain original research. The line you included fails on all three counts. If it's clear to you then I'm pleased for you. That doesn't mean that it will be clear to the casual reader. — Fly by Night (talk) 13:17, 5 October 2010 (UTC)[reply]

What specifically do you feel is not justified here? I don't see anything that can credibly be called original research, so obviously something is not being communicated. Note that uncontroversial knowledge does not generally require a citation (see Wikipedia:SCICITE#Uncontroversial knowledge). I was about to add this to my original post before you replied to it. Also, I don't recall using the phrase "as we all know" in the article, just in the discussion page. If this isn't something known to you, then I would recommend more readings in topology. Kelley's "General topology" is a standard reference and textbook. Sławomir Biały (talk) 13:20, 5 October 2010 (UTC)[reply]

This isn't the right attitude to have. Please do not insult my intelligence and please do not try to be condescending. Please find another reference that justifies the step. This is not a graduate research text, it is an encyclopedia for the casual reader. The idea is that people understand the article without having to read Kelley's "General topology". Maybe you could find the appropriate pages in Kelley's "General topology" and add those as a reference? — Fly by Night (talk) 13:23, 5 October 2010 (UTC)[reply]

You have thrown the WP:OR gauntlet. I now ask you to explain exactly what original research has been committed. I don't think there is any controversial knowledge involved here: I have merely tried to explain "topology generated by..." in a less telegraphic manner than Steen and Seebach. Is the issue that you find the phrase "coarsest topology" cryptic? This can be fixed with copyediting, but is not original research by any reasonable stretch. Sławomir Biały (talk) 13:29, 5 October 2010 (UTC)[reply]

It requires a lot of work to show that "The basis sets are simply cosets of subgroups of the integers" implies that "The evenly spaced integer topology is the coarsest topology that includes as open subsets the family of all arithmetic progressions: that is, arithmetic progressions are a subbase (and, in fact, a base) for the topology". You have used a lot of information that is not contained on pp 80 − 81 of the reference; and so an additional reference would be appropriate. I shall repeat: Maybe you could find the appropriate pages in Kelley's "General topology" and add those as a reference? It would improve the comprehensibility and accessibility of the article greatly. — Fly by Night (talk) 13:43, 5 October 2010 (UTC)[reply]

"It requires a lot of work..." No, it doesn't. It follows from the definition of a base. (Unless you are objecting to the term "coarsest" here? Again, I don't really understand what the issue is. Could you please explain? I've added a general reference on topology. Is that what you want?) Sławomir Biały (talk) 13:57, 5 October 2010 (UTC)[reply]

I have expanded the sentence to several independent sentences. Does this address your concern yet? If not, please state the concern more clearly. Sławomir Biały (talk) 14:02, 5 October 2010 (UTC)[reply]

The irony in this now-ancient discussion is that Sławomir Biały's excellent choice of the term arithmetic progression is far better suited for the casual reader than Steen and Seebach's group-theoretic description. The objections raised are in fact laughable, and Sławomir Biały's patience in dealing with them is admirable. Mathematrucker (talk) 18:49, 6 July 2019 (UTC)[reply]

With that said, I am also grateful to Fly by Night for introducing me to Wikipedia's original research policy, which I was previously unaware of. I understand the reason for having such a policy; it's just that its enforcement wasn't called for in this particular instance. Mathematrucker (talk) 19:01, 6 July 2019 (UTC)[reply]