Talk:Baire space

message: I've seen that several authors define the Baire space to be NN, i.e. the irrationals.  Might need a disambiguation page eventually.  Revolver
Yes, I've seen that too (but only after I started this page!)
For now, I'll just add the other definition, but we may well end up splitting them eventually.
-- Toby Bartels 03:31, 11 Dec 2003 (UTC)
thread_title:  Definition 

message: I merged this page with Baire category theorem because I think both articles are too short and too closely related to be discussed on separate pages.  I killed the purple boxes around the definitions and inserted some standard headings.  Although the boxes looked nice I think the headings yield a better visual structure and standard heading like Definition and Examples provide the reader with faster access to relevant information.  I tried to reorder and expand the material a bit to make it clearer but I am not sure I have succeeded.  Anyway I intend to spend some more time working on this page the next few days.  MathMartin 21:29, 27 Feb 2005 (UTC)
thread_title: Merged with [[Baire category theorem]]

message: I understand the principle that the original author's spelling preferences should be kept, but I got to this page via a link from meager set, and then couldn't find "meager" in the page.  So I've kept "meagre" as the primary spelling in deference to the principle, but added the Yank spellings as an aid to the wayfarer.  --Trovatore 8 July 2005 22:45 (UTC)
:See Wikipedia:Manual of Style#National_varieties of English.  There's really no point in using both spellings - it's easy to see that "meager" is the American way of spelling "meagre" (or equally that "meagre" is the British way of spelling "meager"), and including both just clutters up the article.  The general principle is that if there is no reason to use one or the other (true in this case), the first editor's preference should be used.  http://en.wikipedia.org/w/index.php?title=Baire_space&direction=next&oldid=834287 uses "meagre", so we go with British spelling.  Hairy Dude 22:59, 15 January 2007 (UTC)
thread_title:  American v. British spelling 

message: An alternative definition of baire space: "Every intersection of countably many dense open sets is dense."
This seems unreasonable to me.  Take for example the collection of sets  \ A_p=\mathbb Q + \frac{\pi}{p}, (where p is rational) the shift of the rationals by a non-rational number.  This collection is pairwise disjoint, and therefore  \bigcap_p A_p=\emptyset  which is not dense.  Am I wrong? --Yohai.bs 10:53, 20 July 2007 (UTC)
replies: text: but those sets are "too small": they ain't open.  Mct mht 06:02, 24 July 2007 (UTC)

text: that is why openness is crucial (the intersection of the rationals and irrationals in R is not dense but this does not imply that R is not a Baire space).
Topology Expert (talk) 04:44, 31 October 2008 (UTC)
thread_title:  Question 

message: I just removed the sentence
It should be pointed out that any space containing an isolated point is a Baire space, because an isolated point is its own interior.
because it is false.  It is true that an isolated point is its own interior, but that does not make the space a Baire space!
If you take a non-Baire space (like the positive rational numbers) and add a single isolated point (like -1), then you will NOT get a Baire space! (The original space is an open subset of the new space with the additional point.  If the new space was a Baire space, the original one would also be one...)
--131.234.106.197 (talk) 11:27, 19 May 2008 (UTC)
thread_title:  Any space with an isolated point is a Baire space 

message: "Baire space is a topological space which, intuitively speaking, is very large" — really? A one-dimensional closed interval, is it "very large"? But wait; a finite set of points (even a single point), are they "very large"? What a strange intuition... Boris Tsirelson (talk) 11:02, 17 September 2013 (UTC)
replies: text: I agree, it is not a great description. I rewrote the lead to be a bit more concrete. See if you find it more reasonable. --Mark viking (talk) 12:58, 17 September 2013 (UTC)
replies: text: Better; but I still wonder: finite sets of points (even a single point), are they "very large"? Boris Tsirelson (talk) 20:40, 17 September 2013 (UTC)
thread_title:  Very large, is it?