Geodesic
k-Discreteness and k-Analytic Sets
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 331-341

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

All spaces considered here are metrizable. k will always denote an infinite cardinal. The successor of k will be denoted by k+.Of particular interest will be the Baire spaces where each Tn is a discrete space of cardinal k. The product topology on B(k) is the same as the topology given by the (complete) “first-difference” metric, p : p(s, t) = 1/n if Si = ti for 1 ≦ i ≦ n —1 and sn = tn. A great deal of information about these spaces can be found in [4].A subset A of X is called k-analytic (in X) if there exist, for each t ∈ B(k), closed subsets F(t1), ..., F(t 1, ..., tn), ... of X such that 
Freiwald, Ronald C. k-Discreteness and k-Analytic Sets. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 331-341. doi: 10.4153/CJM-1980-025-3
@article{10_4153_CJM_1980_025_3,
     author = {Freiwald, Ronald C.},
     title = {k-Discreteness and {k-Analytic} {Sets}},
     journal = {Canadian journal of mathematics},
     pages = {331--341},
     year = {1980},
     volume = {32},
     number = {2},
     doi = {10.4153/CJM-1980-025-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-025-3/}
}
TY  - JOUR
AU  - Freiwald, Ronald C.
TI  - k-Discreteness and k-Analytic Sets
JO  - Canadian journal of mathematics
PY  - 1980
SP  - 331
EP  - 341
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-025-3/
DO  - 10.4153/CJM-1980-025-3
ID  - 10_4153_CJM_1980_025_3
ER  - 
%0 Journal Article
%A Freiwald, Ronald C.
%T k-Discreteness and k-Analytic Sets
%J Canadian journal of mathematics
%D 1980
%P 331-341
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-025-3/
%R 10.4153/CJM-1980-025-3
%F 10_4153_CJM_1980_025_3

[1] 1. El'kin, A., A-sets in complete metric spaces, Soviet Math. Dokl. 8 (1967), 874–877. Google Scholar

[2] 2. Hansell, R., Borel measurable mappings for nonseparable metric spaces, Trans. Amer. Math. Soc. 161 (1971), 145–169. Google Scholar

[3] 3. Lasnev, N., Continuous decompositions of collectively normal spaces, Soviet Math. Dokl. 188 (1967), 1069–70. Google Scholar

[4] 4. Kuratowski, K., Topology, v.1 (Academic Press, New York, 1966). Google Scholar

[5] 5. Stone, A. H., Non-separable Borel sets, Rozprawy Matematyczne 28, Warsaw (1962). Google Scholar

[6] 6. Stone, A. H., On a-discreteness and Borel isomorphism, Amer. J. Math. 85 (1963), 655–666. Google Scholar

[7] 7. Stone, A. H., Kernel constructions and Borel sets, Trans. Amer. Math. Soc. 107 (1963), 58–70. Google Scholar

[8] 8. Stone, A. H., Non-separable Borel sets, II, Gen. Top. and Appl. 2 (1972), 249–270. Google Scholar

[9] 9. Pol, R., Note on decompositions of metrizable spaces, I, Fund. Math. 95 (1977), 95–103. Google Scholar

[10] 10. Pol, R., Note on decompositions of metrizable spaces, II, Fund. Math. 100 (2) (1978), 129–143. Google Scholar

[11] 11. Preiss, D., Completely additive disjoint system of Baire sets is of bounded class, Comm. Math. Univ. Carolina. 15 (1975), 341–344. Google Scholar

Cité par Sources :