伪紧空间的Ascoli定理
Ascoli's theorem for pseudocompact spaces
摘要：
一个吉洪诺夫空间$X$称为（{ \em依序}）{ \em Ascoli}，如果每个紧子集（分别为收敛序列）是等度连续的，其中$C_k(X)$表示$X$上所有实值连续函数的空间，并赋予其紧开拓扑.经典的阿斯科利定理指出每个紧空间都是阿斯科利。证明了伪紧空间$X$是Asoli的当且仅当它是序列Ascoli的当且仅当它是选择性$ω$ -有界的.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
