伪紧性的进一步推广
More generalizations of pseudocompactness
摘要：
我们引入了一个覆盖的概念，取决于两个基数，我们称之为$\mathcal O $ - $ [ μ, λ]$ -紧性，它包括伪紧性和许多其他推广的伪紧性。对于吉洪诺夫空间，伪紧性等价于$\mathcal O $ - $ [ ω, ω ]$ -紧性。给出了$\mathcal O $ - $ [ μ, λ]$ -紧性的几个刻画，并讨论了它与$D$ -伪紧性的关系，其中$D$是超滤子.我们分析了上述概念在产品中的行为。最后，我们表明，我们的结果持有一个更一般的框架，其中紧性定义相对于一个任意家庭的子集的一些拓扑空间$X$。
英文摘要：
We introduce a covering notion depending on two cardinals, which we call $\mathcal O $-$ [ μ, λ]$-compactness, and which encompasses both pseudocompactness and many other generalizations of pseudocompactness. For Tychonoff spaces, pseudocompactness turns out to be equivalent to $\mathcal O $-$ [ ω, ω ]$-compactness. We provide several characterizations of $\mathcal O $-$ [ μ, λ]$-compactness, and we discuss its connection with $D$-pseudocompactness, for $D$ an ultrafilter. We analyze the behaviour of the above notions with respect to products. Finally, we show that our results hold in a more general framework, in which compactness properties are defined relative to an arbitrary family of subsets of some topological space $X$.
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。
