论文标题
副型和开放关系
Paracompactness and Open Relations
论文作者
论文摘要
在插入特性方面，Dowker和Katětov的特征是二次paracompact的正常空间。道克还以封闭的单位间隔来表征他们的产品的正常性。迈克尔使用Dowker-Katětov插入属性来激发他对这些空间的选择。莫里塔以自然的方式扩展了道克的产品表征到所有$τ$ - paraccompact普通空间。在本文中，我们从公开关系的角度来看这些结果。对于这种关系，插入和选择是等效的。此外，我们从凸价的开放关系的选择方面，获得了$τ$ - paraccompact正常空间的自然表征。基于此特征，我们提供了上述结果的简单替代证明。也获得了其他应用程序。
The countably paracompact normal spaces were characterised by Dowker and Katětov in terms of an insertion property. Dowker also characterised them by normality of their product with the closed unit interval. Michael used the Dowker-Katětov insertion property to motivate his selection characterisation of these spaces. Morita extended in a natural way Dowker's product characterisation to all $τ$-paracompact normal spaces. In this paper, we look at these results from the point of view of open relations. Insertions and selections are equivalent for such relations. Furthermore, we obtain a natural characterisation of $τ$-paracompact normal spaces in terms of selections for convex-valued open relations. Based on this characterisation, we give simple alternative proofs of the above mentioned results. Other applications are obtained as well.
