论文标题
$ d^{*} $ - space
The $d^{*}$-space
论文作者
论文摘要
在本文中，我们介绍了$ d^{\ ast} $ - 空格的概念。我们发现强$ d $ - 空格是$ d^{\ ast} $ - 空间，但相反的不变。我们给出一个拓扑空间的特征，使其成为$ d^{\ ast} $ - 空间。我们证明了$ d^{\ ast} $的缩回 - space是$ d^{\ ast} $ - space。我们获得这样的结果：对于任何$ t_ {0} $ space $ x $和$ y $，如果功能空间$ top $ top（x，y）$带有isBell拓扑的$是$ d^{\ ast} $ - $ y $，那么$ y $ as a $ d^{\ ast ast} $ - space。我们还表明，对于任何$ t_ {0} $ space $ x $，如果Smyth Power Space $ Q_ {V}（X）$是$ d^{\ ast} $ - space，则$ x $是$ d^{\ ast ast} $ - space。同时，我们给出一个反例，以说明这一点，对于$ d^{\ ast} $ - space $ x $，smyth power space $ q_ {v}（x）$可能不是$ d^{\ ast ast} $ - space。
In this paper, we introduce the concept of $d^{\ast}$-spaces. We find that strong $d$-spaces are $d^{\ast}$-spaces, but the converse does not hold. We give a characterization for a topological space to be a $d^{\ast}$-space. We prove that the retract of a $d^{\ast}$-space is a $d^{\ast}$-space. We obtain the result that for any $T_{0}$ space $X$ and $Y$, if the function space $TOP(X,Y)$ endowed with the Isbell topology is a $d^{\ast}$-space, then $Y$ is a $d^{\ast}$-space. We also show that for any $T_{0}$ space $X$, if the Smyth power space $Q_{v}(X)$ is a $d^{\ast}$-space, then $X$ is a $d^{\ast}$-space. Meanwhile, we give a counterexample to illustrate that conversely, for a $d^{\ast}$-space $X$, the Smyth power space $Q_{v}(X)$ may not be a $d^{\ast}$-space.
