论文标题
构建几乎伪合并
Construction of nearly pseudocompactification
论文作者
论文摘要
当且仅当$ \ upsilon x \ backslash x $中时，空间几乎是假发的，$βx\ backslash x $。如果我们表示$ k = cl_ {βx}（\ Upsilon x \ backslash x）$，则$ΔX= x \ cup（βx\ backslash k）$被Henriksen和Rayburn \ rayburn \ cite {hr80}几乎是$ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $。 Henriksen和Rayburn使用$βX$的不同特性研究了几乎伪混合的扩展。在本文中，我们的主要动机是独立构建$ x $的伪造扩展，而不使用任何类型的扩展特性$βx$。 $βX$的替代结构是通过将所有$ z $ - 粉料的家人带到$ x $中，然后以合适的方式进行拓扑。在本文中，我们还采用了类似的想法，即从划痕中构建$ΔX$，以某种$ x $的收集收集了所有$ x $，称为$ hz $ -ultrafilters，以及固定的$ z $ -Ultrafilter，然后以类似的方式拓位于$βx。$β$ usesive $ use。
A space is nearly pseudocompact if and only if $\upsilon X\backslash X$ is dense in $βX\backslash X$. If we denote $K=cl_{βX}(\upsilon X\backslash X)$, then $δX=X\cup(βX\backslash K)$ is referred by Henriksen and Rayburn \cite{hr80} as nearly pseudocompact extension of $X$. Henriksen and Rayburn studied the nearly pseudocompact extension using different properties of $βX$. In this paper our main motivation is to construct nearly pseudocompact extension of $X$ independently and not using any kind of extension property of $βX$. An alternative construction of $βX$ is made by taking the family of all $z$-ultrafilters on $X$ and then topologized in a suitable way. In this paper we also adopted the similar idea of constructing the $δX$ from the scratch, taking the collection of all $z$-ultrafilters on $X$ of some kind, called $hz$-ultrafilters, together with fixed $z$-ultrafilter and then be topologized in the similar way what we do in the construction of $βX.$ We have further shown that the extension $δX$ is unique with respect to certain properties.
