The construction of all locally compact extensions |
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Authors: | Valerii K Zaharov |
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Institution: | Mathematics Department, Leningrad Institute of Textile and Light Industry, Leningrad, USSR |
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Abstract: | The paper presents one of the ways to construct all the locally compact extensions of a given Tychonoff space T. First, there proved the “local” variant of the Stone-C?ech theorem on “completely regular” Riesz spaces X(T) of continuous bounded functions on T with no unit function, in general, but with a collection of local units. In Theorem 1 it is proved that all the functions from X(T) can be “completely regularly” extended on the largest locally compact extension βxT. Theorem 3 states, that βxT are presenting, in fact, all the locally compact extensions of T. |
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Keywords: | 54C20 54D35 54D45 46E05 54C40 |
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