Upper case and lower case

Upper case and lower case

[Paul Taylor]

> 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

Re: Upper case and lower case

[James Stasheff]

and then there is the traditon of misassigning priority by nameing the
concept


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RE: Upper case and lower case

[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

RE: Upper case and lower case

[Fred E J Linton]

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

Re: Upper case and lower case

[David V Feldman]

>  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

Re: Upper case and lower case

[Charles Wells]

> 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

Re: Upper case and lower case

[Michael Barr]

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   
> 
> 
> 

Upper case and lower case

[ZHAOD]

 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