Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-30T21:24:37.817Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on pointwise convergence of sequences of analytic sets

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  26 February 2010

Roman Pol
Roman Pol
Affiliation:
Wydziat Matematyki U.W., PKiN IXp., 00-901 Warszawa, Poland.
Get access

Extract

§1. Introduction. In this note we shall discuss a certain dichotomy concerning the pointwise convergence of sequences of analytic sets in completely metrizable separable spaces (Proposition 2.1). The dichotomy is closely related to some reasoning due to W. Szlenk [Sz]; we comment on this in Section 5.1.

MSC classification

Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Research Article
Information
Mathematika , Volume 36 , Issue 2 , December 1989 , pp. 290 - 300
Copyright
Copyright © University College London 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ar1.Arhangelskiĭ, A. V.. The structure and classification of topological spaces and the cardinal invariants. Uspehi Mat. Nauk, 33 (1978), 29–84.Google Scholar
Ar2.Arhangelskiĭ, A. V.. The frequency spectrum of a topological space and the product operation. Trudy Mosk._Mat. Obšč., 40 (1979), 171–206.Google Scholar
A-T.Arhangelskiĭ, A. V. and Tkačuk, V. V.. Function spaces and topological invariants. Izdat. Moskov. Univ. (1985) (in Russian).Google Scholar
Bo.Bourgain, J.. The Szlenk index and operators on C(K) spaces. Bull. Soc Math. Belgique, 31 (1979), 87–117.Google Scholar
B-F-T.Bourgain, J., Fremlin, D. H. and Talagrand, M.. Pointwise compact sets of Bairemeasurable functions. Amer. J. Math., 100 (1978), 845–886.Google Scholar
D-J-O-R.Davies, R. O., Jayne, J. E., Ostaszewski, A. J. and Rogers, C. A.. Theorems of Novikov type. Mathematika, 24 (1977), 97–114.Google Scholar
De.Dellacherie, C.. Capacities and analytic sets, in: Cabal Seminar, 77-79, Springer Lecture Notes in Math., 839 (1981).Google Scholar
G-H.Gillespie, D. C. and Hurwitz, W. A.. On sequences of continuous functions having continuous limits. Trans. Amer. Math. Soc, 32 (1930), 527–543.Google Scholar
G-J.Gillman, L. and Jerison, M.. Rings of continuous functions (Princeton, 1960).CrossRefGoogle Scholar
Ha.Hausdorff, F.. Summen von N1, mengen. Fund. Math., 26 (1936), 241–255.Google Scholar
Ku.Kuratowski, K.. Topology, vol. I, II (Warszawa 1966, 1968).Google Scholar
Ly1,.Lyapunov, A. A.. On multiple separability for the δs-operation. Izv. Akad. Nauk SSSR, 3 (1939), 539–552.Google Scholar
Ly2.Lyapunov, A. A.. On multiple separability for the δs-operation. Dokl. Akad. Nauk SSSR, 53 (1946), 399–402.Google Scholar
Ma.Malyhin, V. I.. On countable spaces having no compactification of countable tightness. Dokl. Akad. Nauk SSSR, 206 (1972), 1293–1296.Google Scholar
Mi.Michael, E.. A quintuple quotient quest. Gen. Topology Appl, 2 (1972), 91–138.CrossRefGoogle Scholar
vM.Mill, J. van. An introduction to αω, in Handbook of Set Theoretic Topology (North Holland, 1984).Google Scholar
No1.Nogura, T.. The product of áαiñ-spaces. Topology Appl., 21 (1985), 251–259.CrossRefGoogle Scholar
No2.Nogura, T.. A counterexample for a problem of Arhangelskiǐ concerning the product of Fréchet spaces. Topology Appl, 25 (1987), 75–80.Google Scholar
Ny.Nyikos, P. J.. Metrizability and the Fréchet-Urysohn property in topological groups. Proc. Amer. Math. Soc, 83 (1981), 793–800.Google Scholar
Ol.Olson, R. C.. Bi-quotient maps, countably bi-sequential spaces, and related topics. Gen. Topology Appl, 4 (1974), 1–28.CrossRefGoogle Scholar
Py.Pytkeev, E. G.. On sequentiality of spaces of continuous functions. Uspehi Mat. Nauk, 37 (1982), 197–198.Google Scholar
Sz.Szlenk, W.. The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces. Studia Math., 30 (1969), 53–61.Google Scholar
Ta.Talagrand, M.. Pettis integral and measure theory. Memoirs Amer. Math. Soc, 51 (1984), Number 307.Google Scholar
Us.Uspenskiǐ, V. V.. On embeddings in function spaces. Dokl. Akad. Nauk SSSR, 242 (1978), 545–548.Google Scholar
Za.Zalcwasser, Z.. Sur une propriete du champ des fonctions continues. Studio Math., 2 (1930), 63–67.CrossRefGoogle Scholar