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] Arhangel’skiĭ , A. V. and Buzyakova , R. Z. , On linearly Lindelöf and strongly discretely Lindelöf spaces , Proc. Amer. Math. Soc. , 127 : 8 ( 1999 ), 2449 – 2458 . [7

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is said to be star P , if for any open cover U of X there is a subspace A ⊂ X with property P such that S t ( A , U ) = X . Therefore, a space X is said to be star Lindelöf , if for any open cover U of X there is a Lindelöf subspace

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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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-Theory Problem Book. Special Features of Function Spaces , Springer , New York , 2014 . [17] U spenskij , V. V. , A topological group generated by a Lindelöf Σ

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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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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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Abstract  

The purpose of this note is to show that there exist two Tychonoff spaces X, Y, a subset A of X and a subset B of Y such that A is weakly almost Lindelf in X and B is weakly almost Lindelf in Y, but A B is not weakly almost Lindelf in X Y.

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A topological space (X, π) is said to be nearly Lindelf if every regularly open cover of (X, π) has a countable subcover. In this paper we study the effect of mappings and some decompositions of continuity on nearly Lindelf spaces. The main result is that a δ-continuous image of a nearly Lindelf space is nearly Lindelf.

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A cardinal λ is called ω -inaccessible if for all µ < λ we have µ ω < λ . We show that for every ω -inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ . This extends an analogous earlier result of ours that only worked for regular λ .

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. , Vermeer , H. 1986 Lindelöf locales and realcompactness Math. Proc. Camb. Phil. Soc. 99 473 – 480 10.1017/S0305004100064410 . [14] Marcus , N. , Realcompactifications of frames , MSc

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