Geodesic
A Functional Analytic Proof of a Selection Lemma
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 441-448

Voir la notice de l'article provenant de la source Cambridge University Press

If r is a mapping of a set X onto a set Y, then a selection for r is a mapping S of Y into X for which r o s is the identity. Analogously, if F is a mapping of a set Y into the power set 2Z of a set Z, then a selection for F is a mapping f of Y into Z such that ƒ(y) is an element of F(y) for all y in Y. These two notions are formally equivalent: Given r mapping X onto Y, define F(y) = r –l(y) and Z = X. Conversely, given F mapping Y into 2Z , define X to be the subset of Y × Z consisting of the pairs (y, z) for which z belongs to F(y), and define r on X by r(y, z) = y. 
Baggett, L. W.; Ramsay, Arlan. A Functional Analytic Proof of a Selection Lemma. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 441-448. doi: 10.4153/CJM-1980-035-x
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[1] 1. Andenaes, P. R., Hahn-Banach extensions which are maximal on a given cone, Math. Ann. 188 (1970), 90–96. Google Scholar

[2] 2. Bourbaki, N., Topologie générale, Chapitre 9, Deuxième edition, (Hermann, Paris, 1958). Google Scholar

[3] 3. Christensen, J. P. R., Topology and borel structure (North Holland, Amsterdam, 1974). Google Scholar

[4] 4. Dixmier, J., Dual et quasi-dual d'une algèbre de Banach involutive, Trans. Amer. Math. Soc. 104 (1962), 278–283. Google Scholar

[5] 5. Effros, E. G., Convergence of closed subsets in a topological space, Proc. Amer. Math. Soc. 16 (1965), 929–931. Google Scholar

[6] 6. Effros, E. G., The Borel space of von Neumann algebras on a separable Hilbert space, Proc. J. Math. 15 (1965), 1153–1164. Google Scholar

[7] 7. Fédérer, H. and Morse, A. P., Some properties of measurable junctions, Bull. Amer. Math. Soc. 40 (1943), 270–277. Google Scholar

[8] 8. Himmelberg, C. J. and Van Vleck, F. S., Selections and implicit function theorems for multifunctions with Souslin graph, Bull. Acad. Polon. Sci. 19 (1971), 911–916. Google Scholar

[9] 9. Kuratowski, C., Topologie, Vol. I, 4th Edition (Polska Akademia Nauk, Warsaw, 1958). Google Scholar

[10] 10. Kuratowski, C. and Maitra, A., Some theorems on selectors and their applications to semicontinuous decompositions, Bull. Acad. Polon. Sci. 22 (1974), 877–881. Google Scholar

[11] 11. Mackey, G. W., Induced representations of locally compact groups I, Ann. Math., Ser. 2. 55 (1952), 101–139. Google Scholar

[12] 12. Mackey, G. W., Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 265–311. Google Scholar

[13] 13. von Neumann, J., On rings of operators, reduction theory, Ann. Math. 30 (1949), 401–485. Google Scholar

[14] 14. Wagner, D. H., Survey of measurable selection theorems, Siam Jour. Control and Optimizatio. 15 (1977), 859–903. Google Scholar

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