# AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE

• Yun, Yong-Sik ;
• Kim, Chang-Il
• Accepted : 2012.06.21
• Published : 2012.08.31
• 54 22

#### Abstract

In this paper, we construct an extension ($kX$, $k_X$) of a space X such that $kX$ is a weakly Lindel$\ddot{o}$ff space and for any continuous map $f:X{\rightarrow}Y$, there is a continuous map $g:kX{\rightarrow}kY$ such that $g|x=f$. Moreover, we show that ${\upsilon}X$ is Lindel$\ddot{o}$ff if and only if $kX={\upsilon}X$ and that for any P'-space X which is weakly Lindel$\ddot{o}$ff, $kX={\upsilon}X$.

#### Keywords

filter;realcompactification;weakly Lindel$\ddot{o}$ff space

#### References

1. J.L. Blasco: Complete bases and Wallman realcompactifications. Proc. Amer. Math. Soc. 75 (1979), 114-118. https://doi.org/10.1090/S0002-9939-1979-0529226-2
2. J.L. Blasco: Complete bases in topological spaces II. Studia Sci. Math. Hung. 24 (1989), 447-452.
3. L. Gillman & M. Jerison: Rings of continuous functions. Van Nostrand, Princeton, New York, (1960).
4. C.I. Kim: Almost P-spaces. Commun. Korean Math. Soc. 18 (2003), 695-701. https://doi.org/10.4134/CKMS.2003.18.4.695
5. J. Porter & R.G. Woods: Extensions and Absolutes of Hausdorff Spaces. Springer, Berlin, (1988).
6. A.I. Veksler: P'-points, P0-sets, P'-spaces. A new class of order-continuous measures and functionals, Soviet Math. Dokl. 14 (1973), 1445-1450.

#### Cited by

1. MINIMAL CLOZ-COVERS OF κX vol.35, pp.2, 2013, https://doi.org/10.5831/HMJ.2013.35.2.303