現代数学の系譜11 ガロア理論を読む27 [無断転載禁止]©2ch.net

**現代数学の系譜11 ガロア理論を読む** · 2016/12/30(金) 14:26:21.65

**現代数学の系譜11 ガロア理論を読む** · 2017/01/14(土) 21:35:28.14

>>468
>「ゲルファント・シロフの定理」というのは、1940年くらいの定理だ。

下記のP53辺りにある。なお、下記２つのうち、スキャナーの質は上が良好で読みやすい。下は出典を示す表紙が１枚ついているのが値打ちだ。

http://www.ams.org/journals/tran/1948-064-01/S0002-9947-1948-0026239-9/S0002-9947-1948-0026239-9.pdf
6.1MB rings of real-valued continuous functions. i - American Mathematical Society E Hewitt 著 - ?1948

http://www-math.bgsu.edu/~warrenb/Courses/Research/mtop/hewitt.pdf
1.6MB [PDF]Rings of Real-Valued Continuous Functions. I E HEWITT 著 - ?1948 Transactions a/the American Mathematical Society

**現代数学の系譜11 ガロア理論を読む** · 2017/01/14(土) 21:46:30.59

>>495
(抜粋)
Part I. General properties of function rings.

5. Definition of βX. A cardinal property of rings E*(X, R) is the fact that for every completely regular space, there exists a unique bicompact Hausdorff space, commonly denoted as βX, having the properties that XEβX, X~ = βX, and S*(X, R) is algebraically isomorphic to &*(βX, R).
The existence and uniquene β of βX were first proved by Stone (see [26, Theorems 78, 79, 88]), by methods dependent upon the theory of representation of topological spaces as maps in Boolean spaces. A second, simpler, proof was given by Cech [7].
A third construction of β, valid for normal spaces only, was obtained by Wallman [31 ], and A. Weil has presented a construction based on the theory of uniform structures [32]. A simplified version of Stone's original construction was given in 1941 by Gelfand and Shilov (see [13]).

Kakutani has given a construction of β based on Banach lattices [18].

Finally, Alexandroff, using a modification of Wallman's construction, has produced a construction of β and of yet more general bicompact TV spaces in which arbitrary regular spaces can be imbedded as dense subsets. (See [l ].)
Spaces βX thus appear as truly protean entities, arising in the most diverse manner from apparently unrelated constructions.
It is not our purpose at the present time to elaborate on the inner connections which obtain among the various constructions of β, or to present any eβential variants thereof.
We shall briefly describe the construction obtained by Gelfand and Shilov [13], with the aim of completing and simplifying their proof and of exhibiting the details of their construction for use in certain applications.

13. I. Gelfand and G. E. Shilov, Uber verschiedene Methoden der Einfuhrung der Topologie in die Menge der maximalen Idealen eines normierten Ringes, Rec. Mat. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 25-38.

つづく

**現代数学の系譜11 ガロア理論を読む** · 2017/01/14(土) 21:46:53.08

つづき

18. Shizuo Kakutani, Concrete representations of abstract (M)-spaces, Ann. of Math. vol.42 (1941) pp. 994-1024.
(引用終り)

**現代数学の系譜11 ガロア理論を読む** · 2017/01/14(土) 21:47:38.67

Shizuo Kakutani 先生が引用されているね