稠密k-可分群是稠密可分的
Densely k-separable compacta are densely separable
摘要：
一个空间有$σ$ -紧性，如果$σ$ -紧子集的闭包决定拓扑.我们考虑一个稠密集的变体，我们称之为稠密k-可分的。我们考虑是否每个稠密k-可分空间都是可分的。有些令人惊讶的答案是，对于紧空间，这个性质意味着每个稠密集都是可分的。该结果的路径依赖于在$π$权重和所有稠密子集的密度之间建立的已知连接，或者更精确地说，依赖于基数不变量$δ(X)$。
英文摘要：
A space has $σ$-compact tightness if the closures of $σ$-compact subsets determines the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether every densely k-separable space is separable. The somewhat surprising answer is that this property, for compact spaces, implies that every dense set is separable. The path to this result relies on the known connections established between $π$-weight and the density of all dense subsets, or more precisely, the cardinal invariant $δ(X)$.
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