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Abstract  

We introduce the concept of relatively almost Lindelf subsets as a generalization of almost Lindelf subspaces. We study various properties of relatively almost Lindelf subsets and investigate the relationship between relatively almost Lindelf subsets and almost Lindelf subspaces. A special interest is given to spaces X in which almost Lindelf subsets relative to X are closed.

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Summary  

A subset Y of a space X is weakly almost Lindelf in X if for every open cover U of X, there exists a countable subfamily  V of  U such that Y ⊆ comp (∩V ). We investigate the relationship between relatively weakly almost  Lindelf subsets and relatively almost  Lindelf subsets, and also study various properties of relatively weakly almost  Lindelf subsets.

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