FUNCTION-SPACES OF COMPLETELY METRIZABLE-SPACES

被引：19
|
作者：
BAARS, J
DEGROOT, J
PELANT, J
机构：
[1] CZECHOSLOVAK ACAD SCI,USTAV MATEMAT,CS-11567 PRAGUE,CZECHOSLOVAKIA
[2] FREE UNIV AMSTERDAM,FAC WISKUNDE & INFORMAT,1081 HV AMSTERDAM,NETHERLANDS
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1993年 / 340卷 / 02期
关键词：
FUNCTION SPACES; COMPLETELY METRIZABLE SPACES;
D O I：
10.2307/2154680
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let X and Y be metric spaces and let phi: C(p)(X) --> C(p)(Y) (resp. phi: 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 obtain that complete metrizability is preserved by l(p) (resp. l(p)*-equivalence) in the class of all metric spaces. This solves Problem 35 in [2] (raised by Arhangel'skii).
引用
收藏
页码：871 / 883
页数：13
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