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On isomorphisms of continuous function spaces

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Abstract

The following theorem, which strengthens the classical theorem of Stone, is proved: If there is an isomorphism φ ofC(X) ontoC(Y) (X, Y-compact) with ∥ φ ∥ · ∥ φ−1 ∥ < 2, thenX andY are homeomorphic.

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References

  1. C. Bessaga and A. Pelczynski,Spaces of continuous functions (IV) (On isomorphical classification of spaces of continuous functions), Studia MathematicaXIX (1960), 53–62.

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  2. M. H. Stone,Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc.41 (1937), 375–481.

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Amir, D. On isomorphisms of continuous function spaces. Israel J. Math. 3, 205–210 (1965). https://doi.org/10.1007/BF03008398

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  • DOI: https://doi.org/10.1007/BF03008398

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