Previous |  Up |  Next


$LJ$-spaces; Lindelöf; $J$-spaces; $L$-map; (countably) compact; perfect map; order topology; connected; topological linear spaces
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.
[1] R. R. Engelking: General Topology. Revised and completed edition, Heldermann Verlag, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[2] Y. Kodama and K. Nagami: Theory of General Topology. Iwanami, Tokyo, 1974. (Japanese)
[3] E. Michael: $J$-spaces. Top. Appl. 102 (2000), 315–339. MR 1745451 | Zbl 0942.54020
[4] E. Michael: A note on closed maps and compact sets. Israel Math. J. 2 (1964), 173–176. DOI 10.1007/BF02759940 | MR 0177396 | Zbl 0136.19303
[5] E. Michael: A survey of $J$-spaces. Proceeding of the Ninth Prague Topological Symposium Contributed papers from the Symposium held in Prague Czech Republic, August 19–25, 2001, pp. 191–193. MR 1906840
[6] J. R. Munkres: Topology. Prentice-Hall, Englewood Cliffs, NJ, 1975. MR 0464128 | Zbl 0306.54001
[7] K. Nowinski: Closed mappings and the Freudenthal compactification. Fund. Math. 76 (1972), 71–83. MR 0324628 | Zbl 0235.54023
[8] L. A. Steen and J. A. Seebach, Jr: Counterexamples in Topology. Springer-Verlag, New York, 1978. MR 0507446
Partner of
EuDML logo