The Tychonoff product theorem for compact Hausdorff spaces does not imply the axiom of choice: a new proof. Equivalent propositions
| dc.contributor.author | Rodríguez Salinas, Baltasar | |
| dc.contributor.author | Bombal Gordón, Fernando | |
| dc.date.accessioned | 2023-06-21T02:03:30Z | |
| dc.date.available | 2023-06-21T02:03:30Z | |
| dc.date.issued | 1973 | |
| dc.description.abstract | The main result of this paper is expressed by its title. The authors also show that the Tihonov product theorem for compact Hausdorff spaces is logically equivalent to some basic theorems in topology and functional analysis, commonly proved using the axiom of choice | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17842 | |
| dc.identifier.issn | 0010-0757 | |
| dc.identifier.officialurl | http://www.collectanea.ub.edu/index.php/Collectanea/article/view/3413/4093 | |
| dc.identifier.relatedurl | http://www.collectanea.ub.edu/index.php/Collectanea | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64735 | |
| dc.journal.title | Collectanea mathematica | |
| dc.language.iso | eng | |
| dc.page.final | 230 | |
| dc.page.initial | 219 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 510.22 | |
| dc.subject.keyword | Product spaces | |
| dc.subject.keyword | Set theory | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | The Tychonoff product theorem for compact Hausdorff spaces does not imply the axiom of choice: a new proof. Equivalent propositions | |
| dc.type | journal article | |
| dc.volume.number | 24 | |
| dcterms.references | BACHMAN, G. and NARICI, L.: Functional Analysis. Academic ess, NewYork, 1966. BADRIKIAN, A.: Seminaire sur les Fonctions Aléatoires Linéaires et les Mesures Cylindriques. Lectures Notes in Math., 139, Springer-Verlag, Berlin, 1970. BOURBAKI, N.: Elements of Mathematics. General Topology, Part.1. Act.Sct. et Ind., 0637, Hermann, Paris, 1966. COHEN, P. J.: Set Theory and the Continuum Hypotesis. W. A. Benjamin,New York, 1966. DAY, M. M.: Normed Linear Spaces. Springer-Verlag, Berlín, 1962. v. DALEN, D. and MONNA, A. F.: Sets and Integration. Walter-Noordhoff, Groningen, 1972. FELGNBR, D.: Models of ZF-Set Theory. Lectures Notes in Mafu., 223,Springer-Verlag, Berlin, 1971. HALPERN, J. D.: The independence of the axiom of choice from the Boolean Prime Ideal Theorem. Fund. Mafu. 55, (1964) 57-66. HAT,PERN, J. D. and LÉVY, A.: The Ordering-Theorem does not imPly the axiom of choice. Notices A.M.S. 11, (1964), 56 HALPERN, J. D. and LÉvy, A.: The Boolean Prime Ideal Theorem does not imPly the axiom of choice. Proceedings of Symp. in pure Math. vol. XIII, Parto I, p. 38-134 (A.M.S. Providence 1971). HENKIN, L. A.: Metamathematical tlzeorems equivalent to the prime ideal theorems for Boolean algebras. Bu11. A.M.S. 60 (1954), 388. HORVÁTH, J.: Topological Vector Spaces and Distributions, l. AddisonWesley Publ. Co. Massachusetts, 1966. KAKUTANI, S.: Concrete representation 01 abstract (M)-spaces. Aun. of Math., 42, (1941), 994-1024. KELLEY, J. L.: The Tychonoll product theorem imPlies the axiom of choice. Fund. Math., 37 (1950), 75-76. KELLEY J. L.: Banach spaces with the extension property Trans. Amer, Math. Soc., 72 (1952), 323-325. LOS, J. and RYLL-NARDZEWSKI, E.: On the application of Tychonolf's theorem in mathematical Prools. Fund. Math. 38 (1957), 233-237. LOS, J. and RYLL-NARDZEWSKI, C.: Ellectiveness 01 the representation theory lor Boolean algebras. Fund. Math. 41 (1954), 49-56. NACHBIN, L.: A theorem 01 the Hahn-Banach type. Trans. Amer. Math.Soc., 68 (1950), 28-46. MARcZEWSKI, E. (SZPILRAJN): Sur l'extension de l'ordre partiel. Fund. Math. 16 (1930), 386-389. RUBIN, J. E.: Set Theory lor the Mathematician. Rolden-Day, San Francisco, 1967. RUBIN, R. and Scon, D.: Some topological theorems equivalent to the Boolean prime ideal theorem. BuI!. A.M.S. 60 (1954), 389. SCHAEFER, R. R.: Topological Vector Spaces. Springer-Verlag, Berlin, 1970. SCOTT, D.: Prime Ideal theorems lor rings, lattices and Boolean algebras. Bull. A.M.S. 60 (1954), 390. SIKORSKI, R.: Boolean algebras (Appendix). Springer-Verlag, Berlin, 1964. SIERPINSKI, W.: Zarys terji mnogosci. Warszawa, 1928. TARSKI, A.: Prime ideal theorems lor Boolean algebras and the axiom of choice. Bull. A.M.S. 60 (1954), 390. TARSKI, A.: Prime ideal theorems lor set algebras and ordering principIes. Bull. A.M.S. 60 (1954), 391. TARSKI, A.: Prime ideal theorems lor set algebras and the axiom of choice. Bull. A.M.S. 60 (1954), 391. | |
| dspace.entity.type | Publication |
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