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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rdfs:label	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)
rdfs:comment	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)
dcterms:subject	Types of functions Banach spaces Complex analysis Continuous mappings Functional analysis Real analysis
Wikipage page ID	17560674 (xsd:integer)
Wikipage revision ID	1057637842 (xsd:integer)
Link from a Wikipage to another Wikipage	Types of functions Banach spaces Homomorphism Relatively compact Riesz–Markov–Kakutani representation theorem Uniform norm Vector space Initial topology Positive linear functional Compact space Compact support Complete space Complex numbers Continuous dual space Continuous functions Mathematical analysis Measure theory Subring Closure (topology) Equicontinuous Bounded set Locally compact Stone–Weierstrass theorem Functional analysis Maximal ideal Banach–Alaoglu theorem Topology Weak topology Hausdorff space Banach algebra Normed space Cauchy sequence Complex conjugation Uniform convergence Radon measure Regular measure Ba space Arzelà–Ascoli theorem Complex analysis Continuous mappings Functional analysis Real analysis Homeomorphism Borel measure Real numbers Reflexive space Total variation Separating set Urysohn's lemma Schwartz space Vague topology Weak* topology Gelfand transform
sameAs	Continuous functions on a compact Hausdorff space Continuous functions on a compact Hausdorff space Continuous functions on a compact Hausdorff space Continuous functions on a compact Hausdorff space Continuous functions on a compact Hausdorff space
dbp:wikiPageUsesTemplate	dbt:Banach_spaces dbt:Citation dbt:Harv dbt:Reflist dbt:Functional_analysis dbt:Rudin_Walter_Functional_Analysis
has abstract	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)
prov:wasDerivedFrom	wikipedia-en:Continuous_functions_on_a_compact_Hausdorff_space?oldid=1057637842&ns=0
page length (characters) of wiki page	6894 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Continuous_functions_on_a_compact_Hausdorff_space
is Link from a Wikipage to another Wikipage of	Real-valued function C(X) Equicontinuity Stone–Weierstrass theorem Complete metric space Tight span Arzelà–Ascoli theorem Continuous functions on a compact hausdorff space Space of continuous bounded functions Peter–Weyl theorem
is Wikipage redirect of	C(X)

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