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- W4309796600 abstract "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." @default.
- W4309796600 created "2022-11-29" @default.
- W4309796600 creator A5086227868 @default.
- W4309796600 date "2022-11-19" @default.
- W4309796600 modified "2023-09-25" @default.
- W4309796600 title "The $d^{*}$-space" @default.
- W4309796600 doi "https://doi.org/10.48550/arxiv.2211.10626" @default.
- W4309796600 hasPublicationYear "2022" @default.
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