Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Into isomorphisms of spaces of continuous functions


Author: Krzysztof Jarosz
Journal: Proc. Amer. Math. Soc. 90 (1984), 373-377
MSC: Primary 46E25; Secondary 54C35
DOI: https://doi.org/10.1090/S0002-9939-1984-0728351-2
MathSciNet review: 728351
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ X$ and $ Y$ are locally compact Hausdorff spaces and $ T$ is a linear map from an extremely regular subspace of $ {C_0}\left( X \right)$ into $ {C_0}\left( Y \right)$ such that $ \vert\vert T \vert\vert\vert\vert {{T^{ - 1}}} \vert\vert < 2$, then $ X$ is a continuous image of a subset of $ Y$.


References [Enhancements On Off] (What's this?)

  • [1] D. Amir, On isomorphism of continuous function spaces, Israel J. Math. 3 (1965), 205-210. MR 0200708 (34:596)
  • [2] Y. Benyamini, Small into-isomorphisms between spaces of continuous functions, Proc. Amer. Math. Soc. 83 (1981), 479-485. MR 627674 (82j:46033)
  • [3] M. Cambern, On isomorphisms with small bound, Proc. Amer. Math. Soc. 18 (1967), 1062-1066. MR 0217580 (36:669)
  • [4] B. Cengiz, A generalization of the Banach-Stone theorem, Proc. Amer. Math. Soc. 40 (1973), 426-430. MR 0320723 (47:9258)
  • [5] W. Holsztyński, Continuous mappings induced by isometries of spaces of continuous functions, Studia Math. 26 (1966), 133-136. MR 0193491 (33:1711)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E25, 54C35

Retrieve articles in all journals with MSC: 46E25, 54C35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0728351-2
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society