The $d^{}$-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 o...
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Published in | Electronic Notes in Theoretical Informatics and Computer Science Vol. 2 - Proceedings of... |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
21.03.2023
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Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 2969-2431 2969-2431 |
DOI: | 10.46298/entics.10354 |