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

Cardinals of all Generating Subsets in Semigroup of all Binary Relations on an Infinite set and Its Certain Subsemigroup

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。

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) & f is a function,|F(X)=f: f∈|P(X) & domain(f)=X, Sym(X)=φ: φ is a bijection on X.