Continuous functions on a compact Hausdorff space
In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by , is a vector space with respect to the pointwise addition of functions and scalar multiplication by constants. It is, moreover, a normed space with norm defined by the uniform norm. The uniform norm defines the topology of uniform convergence of functions on . The space is a Banach algebra with respect to this norm.
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Continuous functions on a compact Hausdorff space
In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by , is a vector space with respect to the pointwise addition of functions and scalar multiplication by constants. It is, moreover, a normed space with norm defined by the uniform norm. The uniform norm defines the topology of uniform convergence of functions on . The space is a Banach algebra with respect to this norm.
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In mathematical analysis, and ...... ra with respect to this norm.
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数学の解析学、特に函数解析学の分野において、実数あるいは複素 ...... 義する。空間 C(X) はこのノルムに関してバナッハ環である
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In mathematical analysis, and ...... ra with respect to this norm.
@en
数学の解析学、特に函数解析学の分野において、実数あるいは複素 ...... 義する。空間 C(X) はこのノルムに関してバナッハ環である
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Continuous functions on a compact Hausdorff space
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コンパクトハウスドルフ空間上の連続函数
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