论文标题
Isbell-Mrówka空间的几乎典型
Almost-normality of Isbell-Mrówka spaces
论文作者
论文摘要
我们探索了Isbell-Mrówka空间和一些相关概念的几乎正常。我们使用强迫提供了一个几乎不正常的示例，几乎几乎是不相交的家族，探索了Isbell-Mrówka空间中半正态性的概念，定义了强烈$（\ Aleph_0，<\ alphfrak c）$的概念，几乎是偏见的家庭，并证明了完全可分离的$ $ $ $ $ $ $ $ \ alleph_0，<al eleph $ \ alleph ^ alleph ^ alleph ^ alleph ^ alleph y。 $ \ Mathfrak S = \ Mathfrak C $和$ \ Mathfrak B = \ Mathfrak C $。我们还提供了一个几乎不正常的伪造空间的示例，该伪造空间并非算是紧凑，从而回答了P. szeptycki和S. garcia-balan的问题。
We explore almost-normality in Isbell-Mrówka spaces and some related concepts. We use forcing to provide an example of an almost-normal not normal almost disjoint family, explore the concept of semi-normality in Isbell-Mrówka spaces, define the concept of strongly $(\aleph_0, <\mathfrak c)$-separated almost disjoint families and prove the generic existence of completely separable strongly $(\aleph_0, <\mathfrak c)$-almost disjoint families assuming $\mathfrak s=\mathfrak c$ and $\mathfrak b=\mathfrak c$. We also provide an example of a Tychonoff almost-normal not normal pseudocompact space which is not countably compact, answering a question from P. Szeptycki and S. Garcia-Balan.
