Function spaces of completely metrizable spaces-Reference-Cited by-同舟云学术

Function spaces of completely metrizable spaces

Published:1993 Issue:2 Volume:340 Page:871-883
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Baars Jan,de Groot Joost,Pelant Jan

Abstract

Let X X and Y Y be metric spaces and let ϕ : C p ( X ) → C p ( Y ) \phi :{C_p}(X) \to {C_p}(Y) (resp. ϕ : C p ∗ ( X ) → C p ∗ ( Y ) \phi :C_p^\ast (X) \to C_p^\ast (Y) ) be a continuous linear surjection. We prove that Y Y is completely metrizable whenever X X is. As a corollary we obtain that complete metrizability is preserved by l p {l_p} (resp. l p ∗ l_p^\ast -equivalence) in the class of all metric spaces. This solves Problem 35 in [2] (raised by Arhangel’skiĭ).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1993-340-02/S0002-9947-1993-1160154-X/S0002-9947-1993-1160154-X.pdf

Reference18 articles.

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2. \bysame, Problems in 𝐶_{𝑝}-theory, Open Problems in Topology, (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, pp. 601-615.

3. An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces;Baars, Jan;Comment. Math. Univ. Carolin.,1988

4. On the 𝑙-equivalence of metric spaces;Baars, Jan;Fund. Math.,1991

5. A theorem on function spaces;Baars, Jan;Proc. Amer. Math. Soc.,1989

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