References
Čoban, M.M.: Multivalued mappings and Borel sets I. Trudy Moskov. Mat. Obšč.22, 229–250 (1970) [=Transl. Moscow Math. Soc.22, 258–280 (1970)]
Freiwald, R.C.: Images of Borel sets andk-analytic sets. Fund. Math.75, 35–46 (1972)
Fleissner, W.G.: An axiom for nonseparable Borel theory. Trans AMS251, 309–328 (1979)
Hansell, R.W.: Borel measurable mappings for nonseparable metric spaces. Trans. AMS161, 145–169 (1971)
Hansell, R.W.: On Borel mappings and Baire functions. Trans. AMS194, 195–211 (1974)
Hansell, R.W., Jayne, J.E., Rogers, C.A.: Piece-wise closed functions and almost discretely σ-decomposable families. To appear
Jayne, J.E., Rogers, C.A.: Fonctions et isomorphismes boréliens du premier niveau. C.R. Acad. Sci. Paris Sér. A291, 351–354 (1980)
Jayne, J.E., Rogers, C.A.: Fonctions fermées en partie. C.R. Acad. Sci. Paris Sér. A291, 667–670 (1980)
Jayne, J.E., Rogers, C.A.: Piece-wise closed functions. Math. Ann.255, 499–518 (1981)
Jayne, J.E., Rogers, C.A.: First level Borel functions and isomorphisms. J. Math. Pure Appl.61, 177–205 (1982)
Jayne, J.E., Rogers, C.A.: The invariance of the absolute Borel classes, Convex analysis and optimization. Research Notes in Math., No. 57, pp. 118–151. London: Pitman 1982
Kaniewski, J., Pol, R.: Borel measurable selectors for compact-valued mappings in the non-separable case. Bull. Acad. Polon.23, 1043–1050 (1975)
Kuratowski, K.: Topology I. New York: Academic Press 1966
Rogers, C.A., Jayne, J.E., Dellacherie, C., Topsøe, F., Hoffmann-Jørgensen, J., Martin, D.A., Kechris, A.S., Stone, A.H.: Analytic sets. London: Academic Press 1980
Saint-Raymond, J.: Fonctions boréliennes sur un quotient. Bull. Sci. Math.100, 141–147 (1976)
Taîmanov, A.D.: On closed mappings I. Mat. Sb.,36, 349–352 (1955)
Vaînšteîn, I.A.: On closed mappings on metric spaces. Dokl. Akad. Nauk. SSSR57, 319–321 (1947)
Vaînšteîn, I.A.: On closed mappings. Učen. Zap. Moskov. Univ.155, 3–53 (1952)
Hansell, R.W.: On characterizing non-separable analytic and extended Borel sets as types of continuous images. Proc. London Math. Soc.28, 683–699 (1974)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jayne, J.E., Rogers, C.A. Invariance of borel classes in metric spaces. Math. Ann. 263, 323–341 (1983). https://doi.org/10.1007/BF01457135
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01457135