Isomorphism Problems for the Baire Function Spaces of Topological Spaces
Serdica Mathematical Journal, Tome 24 (1998) no. 1, pp. 5-20
Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library
Let a compact Hausdorff space X contain a non-empty perfect
subset. If α β and β is a countable ordinal, then the Banach space
Bα (X) of all bounded real-valued functions of Baire class α on X is a proper
subspace of the Banach space Bβ (X). In this paper it is shown that:
1. Bα (X) has a representation as C(bα X), where bα X is a compactification
of the space P X – the underlying set of X in the Baire topology
generated by the Gδ -sets in X.
2. If 1 ≤ α β ≤ Ω, where Ω is the first uncountable ordinal number,
then Bα (X) is uncomplemented as a closed subspace of Bβ (X).
These assertions for X = [0, 1] were proved by W. G. Bade [4] and in
the case when X contains an uncountable compact metrizable space – by
F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of
both Bade’s and Dashiell’s methods.
Keywords:
Baire Complemented Banach Space, Baire Function, Scattered Space, Baire Topology, D-Set
@article{SMJ2_1998_24_1_a2,
author = {Choban, Mitrofan},
title = {Isomorphism {Problems} for the {Baire} {Function} {Spaces} of {Topological} {Spaces}},
journal = {Serdica Mathematical Journal},
pages = {5--20},
year = {1998},
volume = {24},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_1998_24_1_a2/}
}
Choban, Mitrofan. Isomorphism Problems for the Baire Function Spaces of Topological Spaces. Serdica Mathematical Journal, Tome 24 (1998) no. 1, pp. 5-20. http://geodesic.mathdoc.fr/item/SMJ2_1998_24_1_a2/