Yin-Zhu Gao, Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China, e-mail: yzgao@jsmail.com.cn
Abstract: In this paper $LJ$-spaces are introduced and studied. They are a common generalization of Lindelof spaces and \(J\)-spaces researched by E. Michael. A space \(X\) is called an \(LJ\)-space if, whenever \(\{A,B\}\) is a closed cover of \(X\) with \(A\cap B\) compact, then \(A\) or \(B\) is Lindelof. 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.
Keywords: $LJ$-spaces, Lindelof, $J$-spaces, $L$-map, (countably) compact, perfect map, order topology, connected, topological linear spaces
Classification (MSC 2000): 54D20, 54D30, 54F05, 54F65
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