论文标题
$ \ text {c}（x）$上的tychonoff空间和环理论顺序
Tychonoff spaces and a ring theoretic order on $\text{C}(X)$
论文作者
论文摘要
减少的环顺序（RR订单）是$ r \ le _ {\ text {rr}} s $的自然部分顺序，如果$ r^2 = rs $可以在$ \ text {c}（x）$的表格中以代数或拓扑进行代数研究。这里的重点放在那些减少的环上，其中每对元素在RR订单中具有最大的含量，这意味着$ x $。如果$ \ text {c}（x）$具有此属性，则$ x $称为rr-ood-ood。令人惊讶的是，本地连接和基本断开的空间共享此属性。在各种拓扑条件下，研究了RR-Good的性质，包括其在笛卡尔产品下的行为。两个RR良好空间的产物可能无法成为RR良好（例如，$β\ Mathbf {r} \ timesβ\ Mathbf {r} $），但是，$ p $ -space和rr good food foodlindelöf空间的产物始终是RR-good。 $ p $ - 空格，$ f $ - 空格和$ u $ - 空间，Glicksberg的定理以及Comfort，Hindman和Negrepontis的工作也是如此。
The reduced ring order (rr-order) is a natural partial order on a reduced ring $R$ given by $r\le_{\text{rr}} s$ if $r^2=rs$. It can be studied algebraically or topologically in rings of the form $\text{C}(X)$. The focus here is on those reduced rings in which each pair of elements has an infimum in the rr-order, and what this implies for $X$. A space $X$ is called rr-good if $\text{C}(X)$ has this property. Surprisingly both locally connected and basically disconnected spaces share this property. The rr-good property is studied under various topological conditions including its behaviour under Cartesian products. The product of two rr-good spaces can fail to be rr-good (e.g., $β\mathbf{R}\times β\mathbf{R}$), however, the product of a $P$-space and an rr-good weakly Lindelöf space is always rr-good. $P$-spaces, $F$-spaces and $U$-spaces play a role, as do Glicksberg's theorem and work by Comfort, Hindman and Negrepontis.
