| dbo:abstract |
In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if and only if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions: 1. * For every limit ordinal γ (i.e. γ is neither zero nor a successor), it is the case that f(γ) = sup {f(ν) : ν < γ}. 2. * For all ordinals α < β, it is the case that f(α) < f(β). (en) 집합론에서 정규 함수(正規函數, 영어: normal function)는 그 도함수를 취할 수 있는, 정의역과 공역이 순서수의 모임인 연속 증가 함수이다. 이를 사용하여 매우 큰 가산 순서수들을 나타낼 수 있다. (ko) |
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| rdfs:comment |
In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if and only if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions: 1. * For every limit ordinal γ (i.e. γ is neither zero nor a successor), it is the case that f(γ) = sup {f(ν) : ν < γ}. 2. * For all ordinals α < β, it is the case that f(α) < f(β). (en) 집합론에서 정규 함수(正規函數, 영어: normal function)는 그 도함수를 취할 수 있는, 정의역과 공역이 순서수의 모임인 연속 증가 함수이다. 이를 사용하여 매우 큰 가산 순서수들을 나타낼 수 있다. (ko) |
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정규 함수 (ko) Normal function (en) |
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