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Keywords:
star-Lindelöf number; the Aquaro number; the absolute Aquaro number; star-Lindelöf; centered-Lindelöf; discretely star-Lindelöf; absolutely discretely star-Lindelöf; $\sigma$-starcompact; pseudocompact
star-Lindelöf number; the Aquaro number; the absolute Aquaro number; star-Lindelöf; centered-Lindelöf; discretely star-Lindelöf; absolutely discretely star-Lindelöf; $\sigma$-starcompact; pseudocompact
Summary:
In this paper, we prove the following statements: (1) For any cardinal $\kappa$, there exists a Tychonoff star-Lindelöf space $X$ such that $a(X)\geq \kappa$. (2) There is a Tychonoff discretely star-Lindelöf space $X$ such that $aa(X)$ does not exist. (3) For any cardinal $\kappa$, there exists a Tychonoff pseudocompact $\sigma$-starcompact space $X$ such that $\operatorname{st}\text{-}l(X)\geq \kappa$.
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