FUNCTION-SPACES OF COMPLETELY METRIZABLE-SPACES

Authors
BAARS J DEGROOT J PELANT J
Citation
J. Baars et al., FUNCTION-SPACES OF COMPLETELY METRIZABLE-SPACES, Transactions of the American Mathematical Society, 340(2), 1993, pp. 871-883
Citations number
18
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
340
Issue
2
Year of publication
1993
Pages
871 - 883
Database
ISI
SICI code
0002-9947(1993)340:2<871:FOCM>2.0.ZU;2-9
Abstract
Let X and Y be metric spaces and let phi: C(p)(X) --> C(p)(Y) (resp. p hi: C(p)(X) --> C(p)*(Y)) be a continuous linear surjection. We prove that Y is completely metrizable whenever X is. As a corollary we obta in that complete metrizability is preserved by l(p) (resp. l(p)-equiv alence) in the class of all metric spaces. This solves Problem 35 in [ 2] (raised by Arhangel'skii).