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Abstract  

In [4], Dlaska introduced the class of almost rc-Lindelf sets and studied some basic properties of such sets. In this paper, we obtain further results concerning almost rc-Lindelf sets. We also introduce new concepts to obtain several mapping properties concerning almost rc-Lindelf sets and almost rc-Lindelf spaces. The property of being an almost rc-Lindelf set is invariant under functions which are slightly continuous and weakly θ-irresolute. It is also shown that the property of being an almost rc-Lindelf space is inverse invariant under functions which are weakly almost open, ω-regular open, and whose fibers are S-sets.

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Abstract  

A space (X, T) is called I-Lindelöf [1] if every cover A of X by regular closed subsets of the space (X, T) contains a countable subfamily A′ such that X = ∪{int (A): AA′}. In this work we introduce the class of I-Lindelöf sets as a proper subclass of rc-Lindelöf sets [3]. We study various properties of I-Lindelöf sets and investigate the relationship between I-Lindelöf sets and I-Lindelöf subspaces. We give a new characterization of I-Lindelöf spaces in terms of this type of sets. Also, we study spaces (X, T) in which every I-Lindelöf set in (X, T) is closed.

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