On F-spaces

Sheldon W. Davis
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引用次数: 2

Abstract

We present the class of Ft-spaces which is a subclass of the class of F-spaces of Harley and Stephenson containing many of the most interesting F-spaces, e.g. the Michael line, the Sorgenfrey line, Aleksandrov's double interval.

We prove that the Ft-spaces satisfy certain covering properties which F-spaces need not satisfy. In particular, (1) every neighborhood Ft-space is subparacompact, and (2) every Ft-space satisfies property L of Bacon. On the other hand, there are examples of neighborhood F-spaces which do not satisfy L.

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在F-spaces
我们提出了一类f -空间,它是Harley和Stephenson的一类f -空间的一个子类,它包含了许多最有趣的f -空间,如Michael线、Sorgenfrey线、Aleksandrov的二重区间。我们证明了f -空间满足某些f -空间不需要满足的覆盖性质。特别地,(1)每个邻域ft空间是次准紧的,(2)每个邻域ft空间满足Bacon的性质L。另一方面,也有邻域f空间不满足L的例子。
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