# perdre son intérêt

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#### zazie

##### Member
The context is pretty mathematical, but maybe you can help me decipher the use of the phrase "perdre son intérêt"?

"Bourbaki a fini par ajouter à son livre sur l'intégration un chapitre portant sur les espaces non localement compacts, mais alors tout ce qui concerne le localement compact perdait son intérêt."

An "espace localement compact" is a "locally compact space," a mathematical object used in topology (in case you know a little higher mathematics...)

• #### Benjy

##### Senior Member
was becoming less important or something like that. ça perdait son interêt -> il n'y avait plus interêt à l'étudier

#### depassage

##### Member
just to check something : is the whole book about the "locally compact space" and only the last chapter about the "not locally (unlocally, lol) compact space" ?

#### la grive solitaire

##### Senior Member
For perdre son intérêt, I'd suggest: he lost interest in it /he no longer took an interest in it/ it no longer interested him

#### Gil

##### Senior Member
Can you confirm that the text is not "perdait de son intérêt"? I think that the meaning might be different if there is a "de" in between.

#### zazie

##### Member
To depassage, yes, only the last chapter is about spaces that are not locally compact.

#### zazie

##### Member
and to Gil, the text is indeed "perdait son intérêt," without "de."

#### le chat noir

##### Senior Member
Probably the first time I regretfully disagree with our lonesome thrush
Here it is about a mathematical theory: since the Bourbaki theory of integration is based on the notion of locally compact spaces, trying to rework it for non-locally compact spaces lead to drop most of the previously established results.

So I think the meaning here is: "all that had been based on local compactness became worthless".

As far as I remember, the example of non-integrable function was the one defined on the set of real numbers as 1 for non-rationals and 0 for rational numbers. The Lebesgue theory of integration, not relying on local compactness, would be able to compute its surface (which amounted, as often in maths, to zero ) while the Bourbaki guys could not, since the function was discontinuous around any point of its domain of definition.
As a preppie back in the mid 80's I must say I had ambivalent feelings toward Bourbaki: so beautifull in its purity and yet an infinite source of headaches .

#### zazie

##### Member
Since "perdait" is in the imperfect, would it be "was becoming worthless"? I'm also confused about the use of "alors." It seems like the sentence is saying that by adding the chapter on non-locally compact spaces, Bourbaki made the rest of the book worthless. But I don't really see how this would make sense. Or maybe "alors" is being used to mean "at that time"?

By the way, for le chat noir, if you're interested in Bourbaki you might want to read the book I'm translating. Its original French title is Bourbaki: une société secrète de mathématiciens, it's by Maurice Mashaal and published by Belin-Pour La Science. It's really interesting, so I'm having a good time translating it (for the American Mathematical Society). Oh, and I think the function you mean is defined as 0 for non-rationals and 1 for rationals, which would make the integral 0 since there are "many more" real numbers than rational numbers (one says the rational numbers have measure 0 in the real numbers).

#### depassage

##### Member
zazie said:
Since "perdait" is in the imperfect, would it be "was becoming worthless"? I'm also confused about the use of "alors." It seems like the sentence is saying that by adding the chapter on non-locally compact spaces, Bourbaki made the rest of the book worthless.
That's the way I interpreted it.
He spent a lot of time to built that theory, and decided to put a chapter about the non-locally compact, as an enlightenment, or something like that, and then, he suddenly realized that the subject of the non-locally compact was way more interesting. He realized while writing that chapter.
And then, maybe they had to re-examine the whole book from the beginning...
I don't think, well, I'm pretty sure "alors" is not use to mean "at that time".
I see "mais alors tout ce qui concerne le localement compact perdait son intérêt." as an unexpected consequence of "Bourbaki a fini par ajouter à son livre sur l'intégration un chapitre portant sur les espaces non localement compacts,"

#### le chat noir

##### Senior Member
LOL sorry, Zazie, my math memories are reduced to heaps of rust in a see of haze .
The funny thing is, I read most interresting stories about Bourbaki in a special issue of "Pour la science", supposedly a French version of "Scientific american", some 5 or 6 years ago. Could it have been the basis for that book?

If I remember the context, the people constituting Bourbaki were criticized for a certain dogmatism and an overly arrogant attitude. They thought they could unify absolutely all the branchs of mathematics into one global, universal theory, and often mocked other scientists when they designed specific theories on limited domains.

When their approach of integration proved significantly weaker than other modern developments of fundamental research (in the 40's or 50's), they did their best to adapt their theory to encompass the new findings. But doing so they had to concede the superiority of Lebesgue's radically different approach, thus highlighting further their failure on this particular point.
The locally compact spaces were supposed to be the place where all functions coukd be inegrated, and conceding that another theory could do better without them was implicitly stating the uselessness of the most numerous results of their own theory.

In this context, the initial sentence seems pretty clear to me: "mais alors" would carry the idea of "doing so[, they implicitely admitted the part about locally compact space was (nearly) useless]"

#### zazie

##### Member
Thanks so much. That does make sense in the context.

You're right, the book is from that issue of Pour la Science. I'm so lucky there's someone here who's read it! Thanks again for the help.

#### la grive solitaire

##### Senior Member
le chat noir said:
So I think the meaning here is: "all that had been based on local compactness became worthless".
Merci chat d'ébène pour ces explications intéressantes, j'apprends des choses. J'étais vraiment à côté de la plaque! <the hermit thrush goes to bone up on Bourbaki >

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