论文标题
$ \ mathbf {e} $ - 在没有选择的公理的情况下，紧凑型扩展
$\mathbf{E}$-compact extensions in the absence of the Axiom of Choice
论文作者
论文摘要
这项工作的主要目的是在没有选择的公理上表明$ \ mathbf {e} $ - $ \ mathbf {e} $的$ \ mathbf {e} $的基本结果 - 尤其是完全规则的空间，尤其是在hewitt practification和banaschewski Compactication上。一些原始结果涉及在给定的零维$ t_1 $ -space上所有连续实际功能的环的特殊子。还显示了有关$ p $ - 空格，baire拓扑和$g_Δ$ - 多流行病的新事实。并非所有调查的语句都有$ \ Mathbf {ZF} $中的证据。某些陈述显示等同于布尔素素理想定理，有些是可数多种选择的公理的后果。
The main aim of this work is to show, in the absence of the Axiom of Choice, fundamental results on $\mathbf{E}$-compact extensions of $\mathbf{E}$-completely regular spaces, in particular, on Hewitt realcompactifications and Banaschewski compactifications. Some original results concern a special subring of the ring of all continuous real functions on a given zero-dimensional $T_1$-space. New facts about $P$-spaces, Baire topologies and $G_δ$-topologies are also shown. Not all statements investigated here have proofs in $\mathbf{ZF}$. Some statements are shown equivalent to the Boolean Prime ideal Theorem, some are consequences of the Axiom of Countable Multiple Choices.
