| 在无穷集合上关系半群、偏函数半群以及函数半群、对称群中生成子集的基数 |
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| 引用本文： | 杨安洲.在无穷集合上关系半群、偏函数半群以及函数半群、对称群中生成子集的基数[J].北京工业大学学报,1991(4). |
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| 作者姓名： | 杨安洲 |
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| 作者单位： | 北京工业大学应用数学系 |
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| 摘 要： | 证明了无穷集合上二元关系半群、一元偏函数半群、一元全函数半群、对称群中的任一生成子集的基数都是相等于这个无穷集的幂集的基数。
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| 关 键 词： | 集合 半群 偏函数 全函数 关系 生成子集 基数 |
Cardinals of all Generating Subsets in Semigroup of all Binary Relations on an Infinite set and Its Certain Subsemigroup |
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| Yang Anzhou.Cardinals of all Generating Subsets in Semigroup of all Binary Relations on an Infinite set and Its Certain Subsemigroup[J].Journal of Beijing Polytechnic University,1991(4). |
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| Authors: | Yang Anzhou |
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| Affiliation: | Department of Applied Mathematics |
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| Abstract: | The following is proved: If X is an infinite set, S is a generating subedt of |R(X) (or |P(X), or |F(X), or Sym(X)), then |S| = 2|X| = exp(|X|), Where |R(X) = {R:R X2}, |P(X)={f:f∈|R(X)& ff is a function}, |F(X) = {f:f∈|P(X) & domain(f) = X}, Sym(X)={ψ:ψ is a bijection on X} . |
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| Keywords: | set semigroup function relation generating subset cardinal number |
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