论文标题
Ascoli定理用于假发空间
Ascoli's theorem for pseudocompact spaces
论文作者
论文摘要
如果每个紧凑型子集（c_k（x）$的每个紧凑型子集（resp。Contrent序列）是公平的，则称为（{\ em sectientally}）{\ em ascoli} {\ em ascoli} {\ em ascoli}是公平的，其中$ c_k（x）$表示所有实现持续的持续功能与x $ comptact the All x $ comptact-comptact oft the the the the topcmop，经典的Ascoli定理指出，每个紧凑的空间都是ascoli。我们表明，伪混合空间$ x $是asoli iff，它是依次是ascoli iff，它是有选择的$ω$结合的。
A Tychonoff space $X$ is called ({\em sequentially}) {\em Ascoli} if every compact subset (resp. convergent sequence) of $C_k(X)$ is equicontinuous, where $C_k(X)$ denotes the space of all real-valued continuous functions on $X$ endowed with the compact-open topology. The classical Ascoli theorem states that each compact space is Ascoli. We show that a pseudocompact space $X$ is Asoli iff it is sequentially Ascoli iff it is selectively $ω$-bounded.
