Decomposability of completely Suslin-additive families
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- by Zdeněk Frolík and Petr Holický
- Proc. Amer. Math. Soc. 82 (1981), 359-365
- DOI: https://doi.org/10.1090/S0002-9939-1981-0612719-6
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Abstract:
It is proved that every point-finite completely Suslin-additive family in the product of a complete metric space by a compact space is $\sigma$-discretely decomposable. Several applications are indicated.References
- Gustave Choquet, Ensembles ${\cal K}$-analytiques et ${\cal K}$-sousliniens. Cas général et cas métrique, Ann. Inst. Fourier (Grenoble) 9 (1959), 75–81 (French). MR 112843, DOI 10.5802/aif.86
- Gustave Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953/54), 131–295 (1955). MR 80760, DOI 10.5802/aif.53
- William G. Fleissner, An axiom for nonseparable Borel theory, Trans. Amer. Math. Soc. 251 (1979), 309–328. MR 531982, DOI 10.1090/S0002-9947-1979-0531982-9
- Zdeněk Frolík, A measurable map with analytic domain and metrizable range is quotient, Bull. Amer. Math. Soc. 76 (1970), 1112–1117. MR 265539, DOI 10.1090/S0002-9904-1970-12584-8 —, The concept of non-separable analytic set, Colloq. Math. Soc. János Bolyai 23, Topology, Budapest, Hungary, 1978, pp. 449-461.
- Z. Frolík, A contribution to the descriptive theory of sets and spaces, General Topology and its Relations to Modern Analysis and Algebra (Proc. Sympos., Prague, 1961) Academic Press, New York; Publ. House Czech. Acad. Sci., Prague, 1962, pp. 157–173. MR 0145471
- Z. Frolík, Analytic and Borelian sets in general spaces, Proc. London Math. Soc. (3) 21 (1970), 674–692. MR 300906, DOI 10.1112/plms/s3-21.4.674
- Zdeněk Frolík, Interplay of measurable and uniform spaces, Proceedings of the International Symposium on Topology and its Applications (Budva, 1972) Savez Društava Mat. Fiz. i Astronom., Belgrade, 1973, pp. 98–101. MR 0375243
- Z. Frolík, Baire sets and uniformities on complete metric spaces, Comment. Math. Univ. Carolinae 13 (1972), 137–147. MR 325903
- Zdeněk Frolík, Four functors into paved spaces, Seminar Uniform Spaces (Prague, 1973–1974) Mat. Ústav Československé Akad. Věd, Prague, 1975, pp. 27–72. MR 0440511 Z. Frolík and P. Holický, $\sigma$-discrete decomposability of completely additive families, Seminar Uniform Spaces (1975-1976), Matematický Ústav ČSAV, Praha, 1976. —, On the non-separable descriptive theory, Fifth Winter School on Abstract Analysis, Matematický Ústav ČSAV, Praha, 1977. —, Analytic and Luzin spaces (non-separable case), preprint. —, Consequences of Luzin separation principle (non-separable case), preprint.
- R. W. Hansell, Borel measurable mappings for nonseparable metric spaces, Trans. Amer. Math. Soc. 161 (1971), 145–169. MR 288228, DOI 10.1090/S0002-9947-1971-0288228-1
- Roger W. Hansell, On the non-separable theory of $k$-Borel and $k$-Souslin sets, General Topology and Appl. 3 (1973), 161–195. MR 319170, DOI 10.1016/0016-660X(73)90017-2
- R. W. Hansell, On characterizing non-separable analytic and extended Borel sets as types of continuous images, Proc. London Math. Soc. (3) 28 (1974), 683–699. MR 362269, DOI 10.1112/plms/s3-28.4.683 P. Holický, Neseparabilní analytické prostory (Non-separable analytic spaces), CSc. thesis, Charles University, 1977.
- J. Kaniewski and R. Pol, Borel-measurable selectors for compact-valued mappings in the non-separable case, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 23 (1975), no. 10, 1043–1050 (English, with Russian summary). MR 410657
- David Preiss, Completely additive disjoint system of Baire sets is of bounded class, Comment. Math. Univ. Carolinae 15 (1974), 341–344. MR 346116 —, Baire class of completely additive systems of Baire sets, Seminar Uniform Spaces (1976-1977), Matematický Ústav ČSAV, Praha, 1977.
- C. A. Rogers, Analytic sets in Hausdorff spaces, Mathematika 11 (1964), 1–8. MR 179750, DOI 10.1112/S0025579300003429
- Maurice Sion, On analytic sets in topological spaces, Trans. Amer. Math. Soc. 96 (1960), 341–354. MR 131507, DOI 10.1090/S0002-9947-1960-0131507-1
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 359-365
- MSC: Primary 28A05; Secondary 54H05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0612719-6
- MathSciNet review: 612719