Subadditive Separating Maps |
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Authors: | E. Beckenstein L. Narici |
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Affiliation: | (1) Mathematics Department, St. John's University, Staten Island, NY, 10301, USA E-mail;(2) Mathematics Department, St. John's University, Jamaica, NY, 11439, USA E-mail |
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Abstract: | Let X and Y denote compact Hausdorff spaces and let K = R (real numbers) or C(complex numbers). C(X) and C(Y) denote the spaces of K-valued continuous functions on X and Y, respectively. A map H : C(X) C(Y) is separating if fg = 0 implies that HfHg = 0. Results about automatic continuity and the form of additive and linear separating maps have been developed in [1], [2], [3], [4], [5], [7], [8], and [10]. In this article similar results are developed for subadditive separating maps. We show (Theorem 5.11) that certain biseparating, subadditive bijections H are automatically continuous. |
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