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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 1st 2014

created computable function (analysis) with the definition of “continuously realizable functions”.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeMar 1st 2014

Excellent. By the way, Baire space directs to a notion of topological space that satisfies the Baire category theorem; I changed to the link in computable function (analysis) (and also at Kleene’s second algebra) to point to irrational number (Toby alerted me to this ambiguity of “Baire space” recently when I was writing on Polish space).

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 1st 2014

Okay, thanks. I have added a disambiguation line at the beginning of Baire space:

This entry is about the class of topological spaces satifiying the Baire category theorem. For the space of irrational numbers underlying Kleene’s second algebra and used in computable analysis, see instead at irrational number.

• CommentRowNumber4.
• CommentAuthorTobyBartels
• CommentTimeMar 5th 2014

That's a rather restrictive note about why one might want that sense of Baire space. What's wrong with the material already in the Idea section? (Maybe it should be more prominently displayed?)

By the way Todd, can you say why it's not completely coincidental that Baire space is a Baire space? When I looked into this, I could find no connection, despite the tantalizing coincidence of names; in particular, Baire's treatise on irrational numbers doesn't mention the complete metric that proves that they form a Baire space.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 5th 2014

Sorry, not sure what you are suggesting. Please feel free to improve as you deem appropriate.

• CommentRowNumber6.
• CommentAuthorTodd_Trimble
• CommentTimeMar 5th 2014

Toby, the ’maybe’ that is there was supposed to attach to both clauses, including the ’not by complete accident’. I haven’t researched the matter to really say for sure one way or the other. I thought it might be better to hedge bets, rather than make the absolute claim that it is pure coincidence. But what you say about Baire’s treatise is interesting; maybe I’ll look into it some more.

You yourself seemed to moderate the claim somewhat where you wrote

but not much should be made of the fact it has the same name. (It is much more important that Baire space is a Polish space than that Baire space is a Baire space. Of course, every Polish space is a Baire space too, so maybe it is important!)

but perhaps I am not understanding what you were driving at there.

• CommentRowNumber7.
• CommentAuthorTobyBartels
• CommentTimeMar 9th 2014

I guess that my ‘maybe’ there was like yours, Todd.

Urs, I will move material from the Idea section to the hatnote.

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