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