# Article

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Keywords:
\$LJ\$-spaces; Lindelöf; \$J\$-spaces; \$L\$-map; (countably) compact; perfect map; order topology; connected; topological linear spaces
Summary:
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.
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