L J -spaces

Yin-Zhu Gao

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 4, page 1223-1237
  • ISSN: 0011-4642

Abstract

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In this paper L J -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 L J -space if, whenever { A , B } is a closed cover of X with A ∩ B compact, then A or B is Lindelöf. Semi-strong L J -spaces and strong L J -spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.

How to cite

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Gao, Yin-Zhu. "$LJ$-spaces." Czechoslovak Mathematical Journal 57.4 (2007): 1223-1237. <http://eudml.org/doc/31190>.

@article{Gao2007,
abstract = {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.},
author = {Gao, Yin-Zhu},
journal = {Czechoslovak Mathematical Journal},
keywords = {$LJ$-spaces; Lindelöf; $J$-spaces; $L$-map; (countably) compact; perfect map; order topology; connected; topological linear spaces; -spaces; -map; (countably) compact; perfect map; order topology; topological linear spaces},
language = {eng},
number = {4},
pages = {1223-1237},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$LJ$-spaces},
url = {http://eudml.org/doc/31190},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Gao, Yin-Zhu
TI - $LJ$-spaces
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1223
EP - 1237
AB - 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.
LA - eng
KW - $LJ$-spaces; Lindelöf; $J$-spaces; $L$-map; (countably) compact; perfect map; order topology; connected; topological linear spaces; -spaces; -map; (countably) compact; perfect map; order topology; topological linear spaces
UR - http://eudml.org/doc/31190
ER -

References

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  2. Theory of General Topology, Iwanami, Tokyo, 1974. (Japanese) (1974) 
  3. J -spaces, Top. Appl. 102 (2000), 315–339. (2000) Zbl0942.54020MR1745451
  4. 10.1007/BF02759940, Israel Math. J. 2 (1964), 173–176. (1964) Zbl0136.19303MR0177396DOI10.1007/BF02759940
  5. 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. (2001) MR1906840
  6. Topology, Prentice-Hall, Englewood Cliffs, NJ, 1975. (1975) Zbl0306.54001MR0464128
  7. 10.4064/fm-76-1-71-83, Fund. Math. 76 (1972), 71–83. (1972) Zbl0235.54023MR0324628DOI10.4064/fm-76-1-71-83
  8. Counterexamples in Topology, Springer-Verlag, New York, 1978. (1978) MR0507446

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