$v$-Lindelöf spaces

Chang Il Kim

The concept of $v$-Lindelöf space is introduced. It is shown that a space $X$ is $v$-Lindelöf if and only if every Wallman realcompactification of $X$ is Lindelöf and that if $X\times Y$ is a $z$-embedded $v$-Lindelöf subspace of $vX\times vY$, then $v(X\times Y)=vX\times vY$.

1. R.A. Aló and H.L. Shapiro $Z$-realcompactifications and normal bases // J. Austral. Math. Soc.V.9--1966p. 489--495

2. R. Blair Spaces in which special sets are $Z$-embedded // Canadian J. Math.V.28--1976p.673--690

3. J.L. Blasko Complete bases and Wallman realcompactifications // Proc. Amer. Math. Soc.V.75–1979p.114–118

4. J.L. Blasko Complete bases in topological spaces // Studia Sci. Math. Hung.V.20–1985p.49–54

5. J.L. Blasko Complete bases in topological spaces, II // Studia Sci. Math. Hung.V.24–1989p.447–452

6. W.W. Comfort On Hewitt realcompactification of a product space // Trans. Amer. Soc.V.181–1968p.107–118

7. L. Gillman and M. Jerison Rings of continuous functions ,addr Van Nostrand, Princeton, New York–1960

8. Irving Glicksberg Stone-Čech compactification of products// Trans. Amer. Math. Soc.V.90–1959p.369–382

9. H. Herrlich and M. Hušek Some open categorical problems in TOP.// Applied Categorical Structure V.1 –1993p.1–19

10. W.G. Mcarthur Hewitt realcompactifications of products // Canadian J. Math.V.22№3–1970p. 645–656

11. J. Porter and R.G. Woods Extensions and absolutes of Hausdorff spaces, Springer,addr Berlin–1988

12. A.K. Steiner and E.F. Steiner Nested generated intersection rings in Tychonoff spaces// Trans. Amer. Math. Soc. V.303–1970 p.779-804

	$v$-Lindelöf spaces
Author	Chang Il Kim Department of Math. Education, Dankook University,Seoul 140-714, Korea
Abstract	The concept of $v$-Lindelöf space is introduced. It is shown that a space $X$ is $v$-Lindelöf if and only if every Wallman realcompactification of $X$ is Lindelöf and that if $X\times Y$ is a $z$-embedded $v$-Lindelöf subspace of $vX\times vY$, then $v(X\times Y)=vX\times vY$.
Keywords	v-Lindelöf space, Wallman realcompactification, z-embedded subspace
DOI	doi:10.30970/ms.9.2.199-204
Reference	1. R.A. Aló and H.L. Shapiro $Z$-realcompactifications and normal bases // J. Austral. Math. Soc.V.9--1966p. 489--495 2. R. Blair Spaces in which special sets are $Z$-embedded // Canadian J. Math.V.28--1976p.673--690 3. J.L. Blasko Complete bases and Wallman realcompactifications // Proc. Amer. Math. Soc.V.75–1979p.114–118 4. J.L. Blasko Complete bases in topological spaces // Studia Sci. Math. Hung.V.20–1985p.49–54 5. J.L. Blasko Complete bases in topological spaces, II // Studia Sci. Math. Hung.V.24–1989p.447–452 6. W.W. Comfort On Hewitt realcompactification of a product space // Trans. Amer. Soc.V.181–1968p.107–118 7. L. Gillman and M. Jerison Rings of continuous functions ,addr Van Nostrand, Princeton, New York–1960 8. Irving Glicksberg Stone-Čech compactification of products// Trans. Amer. Math. Soc.V.90–1959p.369–382 9. H. Herrlich and M. Hušek Some open categorical problems in TOP.// Applied Categorical Structure V.1 –1993p.1–19 10. W.G. Mcarthur Hewitt realcompactifications of products // Canadian J. Math.V.22№3–1970p. 645–656 11. J. Porter and R.G. Woods Extensions and absolutes of Hausdorff spaces, Springer,addr Berlin–1988 12. A.K. Steiner and E.F. Steiner Nested generated intersection rings in Tychonoff spaces// Trans. Amer. Math. Soc. V.303–1970 p.779-804
Pages	199-204
Volume	9
Issue	2
Year	1998
Journal	Matematychni Studii
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