Talk:Hawaiian earring

Correct?

The article states: "It has been shown that $G$ embeds into the inverse limit of the free groups with $n$ generators, $F_n$, where the map from $F_n$ to $F_{n+1}$ is just the one sending the generators of $F_n$ to the first n generators of $F_{n+1}$."

This cannot be correct, as in the inverse limit, there is not a map from $F_n$ to $F_{n+1}$ but rather from $F_{n+1}$ to $F_n$. Indeed, the direct limit given by the natural maps from $F_n$ to $F_{n+1}$ is merely the free group on countably infinitely many generators. — Preceding unsigned comment added by 128.252.164.170 (talk) 10:20, 21 April 2006

When comparing the Hawaiian earring to the infinite wedge of circles $H'$, the article claims that $H'$ " is the one-point compactification of a countable disjoint union of open intervals." This can't be true, since the infinite wedge of circles is not compact (taking the interior of each 1-cell and a small neighborhood of the point at which they meet gives an infinite open cover with no proper subcover). It seems that this has also caused confusion in the article on Quotient Spaces, which refers to R/Z as the Hawaiian earring. BarrySimington 16:02, 8 March 2007 (UTC)

Abelianization of the fundamental group

The article claims the fundamental group's abelianization "has no known simple description", but Katsuya Eda gives such a description on his home page. I just don't know what "Z-adic completion" means. Ntsimp (talk) 04:08, 8 June 2008 (UTC)

Copy

Does it seem strange that what one editor calls a copy of another editor's comment is not a duplication of what the first editor wrote? Hyacinth (talk) 20:52, 31 December 2017 (UTC)

Inline citations

Where does this article lack inline citations? What claims need citing? What kind of citations does the page need? Hyacinth (talk) 20:59, 31 December 2017 (UTC)

There aren't any inline citations in the article at all, just a list of "References". An inline citation is one where a footnote symbol (typically a number in brackets) is found next to the statement it is used to verify, and refers to a specific source found in the References section. They're standard on Wikipedia, but this article doesn't have any yet. Ntsimp (talk) 22:00, 31 December 2017 (UTC)

It is also standard to give an explanation on a talk page when one adds a tag to an article. Hyacinth (talk) 03:24, 9 September 2018 (UTC)

Last sentence of "Higher dimensions" section is problematic

The last sentence of the section Higher dimensions, is as follows:

"For $q\equiv 1{\bmod {(}}k-1)$ and $q>1,$ Barratt and Milnor have proved that the singular homology groups $H_{q}(\mathbb {H} _{k};\mathbb {Q} )$ are not zero and even uncountable."

It appears that one or more words is missing. I hope someone knowledgeable on this subject can fix it.50.205.142.50 (talk) 14:34, 12 May 2020 (UTC)

Why do you think there's a word missing? It's certainly possible, but there doesn't seem to be anything obviously wrong with it. –Deacon Vorbis (carbon • videos) 14:57, 12 May 2020 (UTC)

I just checked the reference, and this is almost exactly what B&M say: "The rational singular homology groups ... are not zero. In fact these groups are not even countable." Maybe the attempt to reword it has left it a bit awkward, but it's certainly correct. –Deacon Vorbis (carbon • videos) 15:10, 12 May 2020 (UTC)

To clarify, there was a logical issue with the original wording. The phrase "are not zero and even uncountable" can be interpreted as being either "are not zero and are not uncountable" or "are not zero but are countable". Dzackgarza (talk)

Requested move 20 June 2021

Hawaiian earring → Infinite earring space – The use of "Hawaiian" in Hawaiian earring originated in the 1950's to identify this space as being "exotic." It has no apparent connection to Hawaiian mathematicians. This particular use of "Hawaiian earring" perpetuations the association of Hawaii and Hawaiian native culture with that which is exotic. This kind of association is no longer acceptable. Moreover, this usage is not universally used in mathematics and there is substantial momentum to do away with it. The term "Hawaiian" no longer has a place being the title term for this page. The title of this page should be changed to "Infinite earring" or "Infinite earring space" and all instances of Hawaiian, perhaps with an exception of a remark clarifying the evolution of the name, should be removed.

It is clear that the opposition has not attempted to actually parse mathematics references and has only conducted a quick internet search of the term "Hawaiian earring" which will obviously pull up the many references that do use this term. This space is called the "infinite earring" on Section 71 of James Munkres' book "Topology." This is the most commonly used textbook for teaching topology. This space is called the "shrinking wedge of circles" in Alan Hatcher's standard book "Algebraic topology." Some older texts use "clamshell." The term "Hawaiian earring" is indeed popular but is not standard.

Jtbrazas (talk) 18:10, 20 June 2021 (UTC)

— Jtbrazas (talk • contribs) has made few or no other edits outside this topic.

• Oppose: Despite the desire to WP:RIGHTGREATWRONGS here, as expressed in the unsourced commentary above by an WP:SPA with practically no edit history, the WP:COMMONNAME of this topic is very clearly "Hawaiian earring". Nearly all of the cited sources have "Hawaiian earring" in their titles, and a web search shows that ""Hawaiian earring" is much more common than "Infinite earring space". There was no evidence given that "Infinite earring space" is used by anyone at all, although by searching I did find one 2015 blog article on the web that uses "Infinite earring" (without appending "space"). Inside that article, it says the subject is also known as "Hawaiian earring". —⁠ ⁠BarrelProof (talk) 19:51, 20 June 2021 (UTC)

• Strongly Support: In this instance, I don't think individual edit history is a material concern. I can attest that this discussion originated among working mathematicians, not all of whom have necessarily have an account or have edited a page on Wikipedia. I think that appealing to its usage in cited sources perhaps misses the point: its usage there is equally problematic and partially due to historical inertia. It's also extremely likely that its popular usage (as evidenced by web searches) is caused by the name of this page, which puts the page in the position of actively doing harm. Since Munkres and Hatcher are by far the standard modern references for this topic and neither use this term, it seems extremely reasonable to move/rename the page here and provide disambiguation as a first effort to fix/change this usage. – Dzackgarza (talk) 18:40, 21 June 2021 (UTC)