Date: Mon, 13 Jul 1998 11:12:57 +0800 From: ZHAOD Subject: categories: Upper case and lower case In mathematics many structures are named after some one's name. For example, Boolean algebra, Hermitian matrices, Hausdorff space, Euclidean space. The first letters of the person's name are usually in upper case. The only exception I have seen are the abelian group and sober space. Does any one know why these two cases are different from others? Thanks Zhao Dongsheng Date: Mon, 13 Jul 1998 14:18:53 -0400 (EDT) From: Michael Barr Subject: categories: Re: Upper case and lower case First off, sober (or sobre) is not an eponym (the fancy name for these). I often write boolean, hausdorff, and euclidean. You sometimes see Abelian. So there are no standards. Note that boolean, euclidean and abelian have adjectival endings (as does Hermitian), while hausdorff does not. In French and German, the two other languages I know somewhat, it is standard that all adjectives be in lower case, that is not so in English. So it comes down to a matter of convention and, basically, familiarity. In physics, it is considered a mark of great respect to achieve lower case status. Nearly all physical constants and units are lower case. But mathematicians do not accept standards conventions and journals make no attempt to enforce uniformity in these matters. On Mon, 13 Jul 1998, ZHAOD wrote: > > In mathematics many structures are named > after some one's name. For example, Boolean > algebra, Hermitian matrices, Hausdorff > space, Euclidean space. The first letters of > the person's name are usually in upper case. > The only exception I have seen are the > abelian group and sober space. Does any one > know why these two cases are different from > others? > > Thanks > > Zhao Dongsheng > > > Date: Mon, 13 Jul 1998 16:37:43 +0100 (BST) From: Paul Taylor Subject: categories: Upper case and lower case > In mathematics many structures are named after some one's name. A questionable practice in many cases, and not necessarily complimentary to the person concerned. For example, G. H. Hardy is famous in genetics for a rather trivial lemma in Bayesian statistics which was his answer to a question over High Table lunch in Trinity one day. How on earth is anyone meant to know what might be meant by "Gauss's Lemma/Theorem/etc"? On the other hand, things can be knocked off inappropriate pedestals by giving them eponymous names. For example, what others call "simple type theory" or "higher order intuitionistic logic" I call "Zermelo type theory" in my book. This has certainly given me a more balanced view of its (limited) importance in mathematics, and I hope to have the same effect on my readers. Given that you're doing it, whether to use a capital depends on national and linguistic custom. The German phrase "hilbertische Raum" looks very peculiar to me, for example. I was brought up to give people capital letters, whether they're nouns or adjectives. I tend *not* to do this if it seems to me that usage of the word has strayed rather a long way from what the person in question actually did, for example "cartesian transformation" for a natural transformation whose naturality squares are pullbacks. Peter Freyd, who of course comes from a different culture from me, will probably tell you his views. Paul Date: Mon, 13 Jul 1998 16:34:30 -0400 (EDT) From: James Stasheff Subject: categories: Re: Upper case and lower case and then there is the traditon of misassigning priority by nameing the concept ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 Date: Mon, 13 Jul 1998 20:48:20 -0400 From: Charles Wells Subject: categories: Re: Upper case and lower case > In mathematics many structures are named >after some one's name. For example, Boolean >algebra, Hermitian matrices, Hausdorff >space, Euclidean space. The first letters of >the person's name are usually in upper case. >The only exception I have seen are the >abelian group and sober space. Does any one >know why these two cases are different from >others? Actually, many people write Abelian group and some people write cartesian product. I have seen boolean algebra, too. Sober spaces are not named after a person. A sober space is a topological space in which every closed subspace that is not the union of proper closed subspaces is the closure of exactly one point. If you are sober then what you see is really there and you don't see double! I heard someone give this explanation at a meeting but I don't know its history. Charles Wells, Department of Mathematics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7058, USA. EMAIL: charles@freude.com. OFFICE PHONE: 216 368 2893. FAX: 216 368 5163. HOME PHONE: 440 774 1926. HOME PAGE: URL http://www.cwru.edu/artsci/math/wells/home.html Date: Wed, 15 Jul 1998 11:25:51 +0200 From: tholen@univaq.it (Walter Tholen) Subject: categories: Hilbertraum Just a brief comment concerning Paul's recent posting. I don't know in which German text he found "hilbertischer Raum", it has at least one mistake in it! Usually one says Hilbertraum, like Banachraum, Frechetraum, etc. Also possible is Hilbertscher Raum (without "i" after t), and hilbertscher Raum may also be acceptable. As far as I remember (I have no relevant reference book at hand at my current location), the rule for making out of a name an adjective by adding sch (and the appropriate e, er - depending on declention) is to keep the capital of the name, unless the term has become absolutely standard (like abelsche Gruppe); to use the lower case is then regarded as an honour to the person in question (Abel). No more linguistics - Cheers, Walter. From: David V Feldman Subject: categories: Re: Upper case and lower case Date: Tue, 14 Jul 1998 10:10:25 -0400 (EDT) > In mathematics many structures are named > after some one's name. For example, Boolean > algebra, Hermitian matrices, Hausdorff > space, Euclidean space. The first letters of > the person's name are usually in upper case. > The only exception I have seen are the > abelian group and sober space. Does any one > know why these two cases are different from > others? > > Thanks > > Zhao Dongsheng > > > Fred Linton explains the term sober space this way: if you haven't been drinking you don't see double (so you don't want any pair of points belonging to the same set of open sets) and you certainly don't see any pink elements (irreducible closed sets with no generic point). David Feldman Date: Wed, 15 Jul 1998 18:38:40 -0500 (EST) From: Fred E J Linton Subject: categories: RE: Upper case and lower case David Feldman erroneously credits to me an insight that is not mine, but Peter Johnstone's. Cf. {Topos Theory}, p. 230: > ... If we regard two distinct points having the same closure > as an instance of double vision (and an irreducible closed set with no > generic point as a species of pink elephant!), then the reason for the > term "sober space" will be apparent. (Thanks, David, but credit where credit is due.) -- Fred Subject: categories: RE: Upper case and lower case Date: Fri, 17 Jul 1998 10:09:01 +0100 (BST) From: "Dr. P.T. Johnstone" > > David Feldman erroneously credits to me an insight that is not mine, but > Peter Johnstone's. Cf. {Topos Theory}, p. 230: > > > ... If we regard two distinct points having the same closure > > as an instance of double vision (and an irreducible closed set with no > > generic point as a species of pink elephant!), then the reason for the > > term "sober space" will be apparent. > > (Thanks, David, but credit where credit is due.) > > -- Fred > I can't claim the credit either: the wording above is mine, but I copied the idea from something written by Bill Lawvere. I can't now find the reference, but I think it may have been in his 1976 Chicago lecture notes on "Variable Sets, Etendu and Variable Structures in Topoi" (of which I no longer have a copy). Peter Johnstone Date: Mon, 20 Jul 1998 16:09:15 +0000 From: s.vickers@doc.ic.ac.uk (Steven Vickers) Subject: categories: Alfred Sober - some recollections Recent mention of sober spaces brought to mind memories of Alfred Philpott Sober, whose sad death from liver failure five years ago ended a long career in topology. Though largely unpublished, it was his work that underlay the notion of what are now known as sober spaces. In Sober's view, points of topological spaces are essentially blurred and hazy: however hard you try to focus on them they always seem to jiggle about a bit - to him "focusing on a point" meant to find it within some _open_ neighbourhood, and these almost always left some room for manoeuvre. He understood the points to be exactly their open neighbourhood filters, and the spaces that would now be called non-sober were trying to impose an over-clear view of reality, making artificial distinctions between what was actually the same thing or trying to deny the existence of something he could see with his own eyes. On the related subject of continuity, he saw its essence as that of a function was that was not unduly upset by this jiggling: as long as the argument didn't jiggle too much, the result wouldn't either, and he liked to demonstrate the idea by carrying a tray of drinks across a crowded room. Though not one of the founders of locale theory, he was aware of the idea and greatly sympathetic to it - though he couldn't see any reason for using the French spelling and pronunciation. Once when in the midst of explaining his ideas the lattice structures started to become manifest and he would excitedly talk about "getting down to the local". He studied initially at Cambridge under the influence of Charles Wells (the Bedford Charles Wells, NOT the well-known category theorist) and his thesis, starting off on Klein bottles, soon took in Gross bottles too. He made his academic home in the University of Portsmouth and was much loved by both his colleagues and his students for his parties and for his never-failing warm welcome "Come in and what'll you have?" He is much missed by all who knew him. Steve Vickers.