论文标题
$ C $ -REALCOMPACT空间的内在特征
Intrinsic characterizations of $C$-realcompact spaces
论文作者
论文摘要
$ C $ -REALCOMPACT空间由Karamzadeh和Quaest的Keshtkar引入。数学。 41（8），2018，1135-1167。我们通过$ c $ c $ stable $ x $的封闭套件的$ x $ $ x $的特征表明$ x $是$ c $ -c $ -realCompact，并且仅当每个$ c $稳定的$ c $稳定的封闭套件中的$ x $中的$ x $中的封闭式家庭都有有限的交叉属性属性。对于任意拓扑空间来说，这是有意义的最后条件，可以作为$ C $ -REALCOMPACT空间的替代定义。我们表明，每个拓扑空间可以作为密集的子空间扩展到具有一些所需的扩展属性的$ C $ -REALCOMPACT空间。引入了类似于$ c $ -RealCompact空间的盟军类别$ CP $ CP $ -COMPACT的空间。该论文在研究了已知的$ c $ realCompact空间的一类班级后结束，可以将其视为$ cp $ compact，用于适当选择的理想理想的$ p $ $ x $的封闭套件。
$c$-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41(8), 2018, 1135-1167. We offer a characterization of these spaces $X$ via $c$-stable family of closed sets in $X$ by showing that $X$ is $c$-realcompact if and only if each $c$-stable family of closed sets in $X$ with finite intersection property has nonempty intersection. This last condition which makes sense for an arbitrary topological space can be taken as an alternative definition of a $c$-realcompact space. We show that each topological space can be extended as a dense subspace to a $c$-realcompact space with some desired extension property. An allied class of spaces viz $CP$-compact spaces akin to that of $c$-realcompact spaces are introduced. The paper ends after examining how far a known class of $c$-realcompact spaces could be realized as $CP$-compact for appropriately chosen ideal $P$ of closed sets in $X$.
