论文标题
分离不良的无限普通产品
Poorly separated infinite normal products
论文作者
论文摘要
紧凑的正常空间的产物是正常的。仅当它是次数的paracrocact且每个有限的子产品的乘积是正常的，而无数的非平凡空间收集的乘积是正常的。如果空间X的所有功率都是正常的，则X是紧凑的：在涉及的空间为T1的情况下提供。在这里，我研究了不需要T1（或常规）的无限产品的情况，扩展或推广这些事实。此外，我证明了一些相关的结果，给出了许多示例，探索了一些替代证明，并与这些发现对类别理论和晶格理论的潜在应用进行了一些猜测。
A product of compact normal spaces is normal; the product of a countably infinite collection of non-trivial spaces is normal if and only if it is countably paracompact and each of its finite sub-products is normal; if all powers of a space X are normal then X is compact: provided in each case that the spaces involved are T1. Here I examine the situation for infinite products not required to be T1 (or regular), extending or generalizing each of these facts. In addition, I prove some related results, give a number of examples, explore some alternative proofs, and close with some speculation regarding potential applications of these findings to category theory and lattice theory.
