From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: Re: Sorting out who's who (was Re: You know you've made it in mathemat
Date: 18 Feb 1998 14:45:55 GMT
In article <6cdbg3$k1o$1@gannett.math.niu.edu>, rusin@vesuvius (Dave Rusin) writes:
>In article <6cconn$hfp$1@netnews.upenn.edu>,
>Matthew P Wiener wrote:
>>In article <6cchlt$fj1$1@gannett.math.niu.edu>, rusin@vesuvius (Dave Rusin) writes:
>>>On a related note, I am unsure as to who the Stone is in
>>> * 06E15 Stone space and related constructions
>>>There are several well-known Stones, but I'm not sure which is most
>>>likely to be known by name in Boolean algebras.
>>Marshall H Stone, "The Theory of Representation for Boolean Algebras",
>>TAMS, v40, (1936), pp 37-111 and "Applications of the Theory of Boolean
>>Rings to General Topology" TAMS v41, (1937) pp 385-471.
>Thank you; this is the kind of thing I wanted to know.
According to Johnstone, these two papers are a major (as in really really
big) landmark in 20th century mathematics. In addition to the carefully
worked out implicitly categorical concepts of universal solution and
adjoint pair, the very idea of constructing a topological representation
for anything algebraic first appears here. The Zariski topology, in fact,
is Stone's construction on not-necessarily-Boolean rings.
v
>>This Stone is also the Stone of the Stone-Cech compactification and the
>>Stone-Weierstrass theorem. He is not, however, the Stone who proved that
>>all metric spaces are paracompact. Who are the other well-known Stones?
>Well, I already knew M.H.Stone = "Stone-Cech" Stone = "Stone-Weierstrass"
>Stone. This Stone has an entry in the History Archive at St. Andrews.
And these two famous results of Stone are in the second paper I cited!
>The metrizability guy is A.H. Stone.
He didn't actually do metrizability, although in the wake of his theorem,
several people saw how to proceed.
> There's an M.G.Stone publishing
>in area 06 in recent years, and I am told Marshall's son David works in
>PL topology.
Yes, but are they "well-known"? I would expect a name like "Stone" to
be common enough. (Actually, I was fishing for something like Gerry
Myerson's response.)
--
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
==============================================================================
From: "NATHANIEL SILVER"
Newsgroups: sci.math
Subject: Re: Sorting out who's who (was Re: You know you've made it in mathemat
Date: 18 Feb 1998 18:48:21 GMT
[previous post quoted -- djr]
Please permit a comment connecting works of Stone and Gelfand.
Paul Halmos characterizes Boolean theory as a discretized snapshot
of all mathematics taken through the wrong end of a telescope.
He claims that "...everything in mathematics has its zero-one
version in Boolean theory." The Boolean version of general topology
is a "curious compromise between the finite and the continuous..."
i.e., the totally disconnected.
The Stone Representation Theorem is the Boolean version of Gelfand
representation theory for commutative C*-algebras, whatever that is.
"Stone is an easy corollary of Gelfand, and the skeleton of the main
steps in the Gelfand proof is visible in the Stone proof...[T]he Gelfand
proof can be arranged so...the Stone proof is its first step, the one that
effects the main construction."
I'm sure this information will not lead to a subtraction from the list
of anyone named Stone.