Geodesic
$LJ$-spaces
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1223-1237.

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In this paper $LJ$-spaces are introduced and studied. They are a common generalization of Lindelöf spaces and $J$-spaces researched by E. Michael. A space $X$ is called an $LJ$-space if, whenever $\lbrace A,B\rbrace $ is a closed cover of $X$ with $A\cap B$ compact, then $A$ or $B$ is Lindelöf. Semi-strong $LJ$-spaces and strong $LJ$-spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.
Classification : 54D20, 54D30, 54F05, 54F65
Keywords: $LJ$-spaces; Lindelöf; $J$-spaces; $L$-map; (countably) compact; perfect map; order topology; connected; topological linear spaces 
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     author = {Gao, Yin-Zhu},
     title = {$LJ$-spaces},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_4_a8/}
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Gao, Yin-Zhu. $LJ$-spaces. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1223-1237. http://geodesic.mathdoc.fr/item/CMJ_2007__57_4_a8/