FUNCTION-SPACES OF COMPLETELY METRIZABLE-SPACES

被引：20

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

页码：871 / 883

页数：13

共 18 条

[1]

Arhangel'skii A.V., 1982, SOVIET MATH DOKLADY, V25, P852

[2]

ARHANGELSKII A, 1990, OPEN PROBLEMS TOPOLO, P601

[3] ON TOPOLOGICAL AND LINEAR HOMEOMORPHISMS OF CERTAIN FUNCTION-SPACES [J].