Compactifications and function algebras
Woodruff, David S.
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 62 (1977), p. 45-51 / Harvested from Biblioteca Digitale Italiana di Matematica

Si costruiscono compattificazioni di uno spazio X usando certe sottigliezze di funzioni su X (le cosiddette algebre di stone complete) che sono valutate in un campo completo separato uniforme k. In tal modo si generalizzano le compattificazioni introdotte da altri autori.

Publié le : 1977-08-01
@article{RLINA_1977_8_63_1-2_45_0,
     author = {David S. Woodruff},
     title = {Compactifications and function algebras},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {62},
     year = {1977},
     pages = {45-51},
     zbl = {0427.54014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1977_8_63_1-2_45_0}
}
Woodruff, David S. Compactifications and function algebras. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 62 (1977) pp. 45-51. http://gdmltest.u-ga.fr/item/RLINA_1977_8_63_1-2_45_0/

[1] Bachman, G., Beckenstein, E., Narici, L. and Warner, S. (1975) - Rings of Continuous Functions with Values in a Topological Field, «Trans. A.M.S.», 204, 91-112. | MR 402687 | Zbl 0299.54016

[2] Berenbom, J. (1973) - Topological Algebras over Valued Fields. Dissertation, Polytechnic Institute of New York. | MR 2623181

[3] Bourbaki, N. (1972) - 1) Commutative Algebra, Addison Wesley, Reading Mass.; (1961) - 2) General Topology, Part 1, Addison Wesley, Reading; (1966) - 3) General Topology, Part 2, Addison Wesley, Reading. | MR 205211

[4] Dugundji, J. (1966) - Topology, Allyn and Bacon, Boston. | MR 193606

[5] Frink, O. (1964) - Compactifications and Semi-Normal Spaces, «Amer. J.Math.», 86, 602-607. | MR 166755 | Zbl 0129.38101

[6] Gelfand, , Raikov, and Shilov, (1964) - Commutative Normed Rings, Chelsea Pub. Co.. | MR 205105

[7] Glllman, L. and Jerison, M. (1960) - Rings of Continuous Functions, D. Van Nostrand, Princeton. | MR 116199

[8] Gordon, H. (1970) - Compactifications by Means of Generalized Ultrafilters, «Ann. Mat. Pura. Appl.», 86 (4), 15-23. | MR 270339

[9] Holladay, J. C. (1957) - A Note on the Stone-Weierstrass Theorem for Quaternions, «Proc. A.M.S.», 8, 656-657. | MR 87047 | Zbl 0077.10501

[10] Kaplansky, I. - Topological Methods in Valuation Theory, «Duke Math. Jour.», 14, 527-541. | MR 22210 | Zbl 0030.01004

[11] Kelly, J. L. (1955) - General Topology, D. Van Nostrand, Princeton. | MR 70144

[12] Mrowka, S. (1973) β-Like Compactifications, «Acta. Math. Acad. Sci. Hung.», 24, 279-287. | MR 341407 | Zbl 0273.54015

[13] Nagami, K. (1970) - Dimension Theory, Academic Press., N. Y.. | MR 271918 | Zbl 0224.54060

[14] Narici, L., Beckenstein, E. and Bachman, G. (1971) - Functional Analysis and Valuation Theory, Marcel Dekker, N. Y.. | MR 361697 | Zbl 0218.46004

[15] Rickart, C. E. (1960) - General Theory of Banach Algebras, D. Van Nostrand, Princeton. | MR 115101 | Zbl 0095.09702

[16] Semadeni, Z. (1971) - Banach Spaces of Continuous Functions, Paristowowe Wydawnictwo Naukowe, Warsaw.

[17] Sultan, A. (1975) - Lattice Realcompactifications, «Ann. Math. Pura. Appl.», 106, 293-303. | MR 410675 | Zbl 0317.54031

[18] Thron, W., (1966) - Topological Structures, Holt Rinehart and Winston, N. Y.. | MR 200892

[19] Warner, S. - Ulaml's Measures Problem, Lecture notes on algebras of continuous functions, Reade College.

[20] Woodruff, D. - Complete Function Algebras with Values in A Uniform Field, to appear. | MR 559008 | Zbl 0489.46056