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As in the previous chapter, the family \(C(X)\) of all real-valued continuous functions on a nonempty compact topological space X is considered with its standard sup-norm, i.e., \(\displaystyle ||f|| = {\mathrm {sup}}\{|f(x)|: x \in X\}\qquad (f \in C(X)). \)

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More on the Function Space \(C(X)\)

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  • 发表日期：

    2025年

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  • Alexander Kharazishvili

摘要

As in the previous chapter, the family \(C(X)\) of all real-valued continuous functions on a nonempty compact topological space X is considered with its standard sup-norm, i.e., \(\displaystyle ||f|| = {\mathrm {sup}}\{|f(x)|: x \in X\}\qquad (f \in C(X)). \)