Baire’s Theorem and Its Consequences
نویسنده
چکیده
We prove Baire’s theorem and its standard consequences: The uniform boundedness principle, the open mapping theorem, and the closed graph theorem.
منابع مشابه
The Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
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