About: Continuous functions on a compact Hausdorff space

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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 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. (en)
  • 数学の解析学、特に函数解析学の分野において、実数あるいは複素数に値を取るコンパクトハウスドルフ空間上の連続函数（コンパクトハウスドルフくうかんじょうのれんぞくかんすう、英: continuous functions on a compact Hausdorff space）の空間は基本的な役割を担う。C(X) と表記されるこの空間は、各点ごとの函数の和と定数によるスカラー倍によってベクトル空間となる。さらに、次で定義される一様ノルムによってノルム線型空間にもなる。 この一様ノルムは、X 上の函数の一様収束の位相を定義する。空間 C(X) はこのノルムに関してバナッハ環である。 (ja)
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  • 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. (en)
  • 数学の解析学、特に函数解析学の分野において、実数あるいは複素数に値を取るコンパクトハウスドルフ空間上の連続函数（コンパクトハウスドルフくうかんじょうのれんぞくかんすう、英: continuous functions on a compact Hausdorff space）の空間は基本的な役割を担う。C(X) と表記されるこの空間は、各点ごとの函数の和と定数によるスカラー倍によってベクトル空間となる。さらに、次で定義される一様ノルムによってノルム線型空間にもなる。 この一様ノルムは、X 上の函数の一様収束の位相を定義する。空間 C(X) はこのノルムに関してバナッハ環である。 (ja)
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  • Continuous functions on a compact Hausdorff space (en)
  • コンパクトハウスドルフ空間上の連続函数 (ja)
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