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首页> 外文期刊>Applied Categorical Structures >Conway’s Question: The Chase for Completeness
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Conway’s Question: The Chase for Completeness

机译：康威的问题：追求完整性

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摘要

We study various degrees of completeness for a Tychonoff space X. One of them plays a central role, namely X is called a Conway space if X is sequentially closed in its Stone–?ech compactification β X (a prominent example of Conway spaces is provided by Dieudonné complete spaces). The Conway spaces constitute a bireflective subcategory Conw of the category Tych of Tychonoff spaces. Replacing sequential closure by the general notion of a closure operator C, we introduce analogously the subcategory Conw C of C-Conway spaces, that turns out to be again a bireflective subcategory of Tych. We show that every bireflective subcategory of Tych can be presented in this way by building a Galois connection between bireflective subcategories of Tych and closure operators of Top finer than the Kuratowski closure. Other levels of completeness are considered for the (underlying topological spaces of) topological groups. A topological group G is sequentially complete if it is sequentially closed in its Ra?kov completion ${ ifmmodeexpandaftertildeelseexpandafter~fi{G}}$ . The sequential completeness for topological groups is stronger than Conway’s property, although they coincide in some classes of topological groups, for example: free (Abelian) topological groups, pseudocompact groups, etc.
机译：我们研究了Tychonoff空间X的不同程度的完整性。其中一个起着核心作用，即如果X在其Stone-Fech压缩βX中顺序关闭，则X称为Conway空间（提供了Conway空间的一个著名例子）由Dieudonné完整空间）。 Conway空间构成Tychonoff空间Tych类别的双反射子类别Conw。用闭包运算符C的一般概念代替顺序闭包，我们类似地引入C-Conway空间的子类别Conw C ，结果又是Tych的双反射子类别。我们显示，可以通过在Tych的双反射子类别和Top的闭包算符比Kuratowski闭包更精细之间建立Galois连接来显示Tych的每个双反射子类别。对于拓扑组的（基础拓扑空间）还考虑了其​​他完整性级别。如果拓扑组G在其Rakov完成$ {ifmmodeexpandaftertildeelseexpandafter〜fi {G}} $中按顺序关闭，则它是按顺序完成的。尽管拓扑组在某些类别的拓扑组中重合，例如自由（Abelian）拓扑组，伪紧缩组等，但拓扑组的顺序完整性要强于Conway的属性。

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