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Lindelöf space; strongly Lindelöf subset; almost Lindelöf subset; strongly almost Lindelöf subset
A subspace $Y$ of a space $X$ is almost Lindelöf (strongly almost Lindelöf) in $X$ if for every open cover $\mathcal U$ of $X$ (of $Y$ by open subsets of $X$), there exists a countable subset $\mathcal V$ of $\mathcal U$ such that $Y\subseteq \bigcup \{\overline V\: V\in \mathcal V\}$. In this paper we investigate the relationships between relatively almost Lindelöf subset and relatively strongly almost Lindelöf subset by giving some examples, and also study various properties of relatively almost Lindelöf subsets and relatively strongly almost Lindelöf subsets.
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