DOI QR코드

DOI QR Code

MINIMAL BASICALLY DISCONNECTED COVERS OF PRODUCT SPACES

Kim Chang-Il

  • Published : 2006.04.01

Abstract

In this paper, we show that if the minimal basically disconnected cover ${\wedge}X_\imath\;of\;X_\imath$ is given by the space of fixed a $Z(X)^#$-ultrafilters on $X_\imath\;(\imath=1,2)\;and\;{\wedge}X_1\;{\times}\;{\wedge}X_2$ is a basically disconnected space, then ${\wedge}X_1\;{\times}\;{\wedge}X_2$ is the minimal basically disconnected cover of $X_1\;{\times}\;X_2$. Moreover, observing that the product space of a P-space and a countably locally weakly Lindelof basically disconnected space is basically disconnected, we show that if X is a weakly Lindelof almost P-space and Y is a countably locally weakly Lindelof space, then (${\wedge}X\;{\times}\;{\wedge}Y,\;{\wedge}_X\;{\times}\;{\wedge}_Y$) is the minimal basically disconnected cover of $X\;{\times}\;Y$.

Keywords

basically disconnected space;covering maps;weakly $Lindel\ddot{o}f$ space

References

  1. J. N. Bourbaki, General Topology, Addison-Wesley, London, 1966
  2. W. W. Comfort, N. Hindman, and S. Negrepontis, F' -spaces and their products with P-spaces, Pacific J. Math. 28 (1969), 489-502 https://doi.org/10.2140/pjm.1969.28.489
  3. M. Henriksen, J. Vermeer, and R. G. Woods, Quasi-F-covers of Tychonoff spaces, Trans. Amer. Math. Soc. 303 (1987), 779-804 https://doi.org/10.2307/2000697
  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. Vermeer, The smallest basically disconnected preimage of a space, Topology Appl. 17 (1984), 217-232 https://doi.org/10.1016/0166-8641(84)90043-9
  6. C. I. Kim, Minimal covers and filter spaces, Topology Appl. 72 (1996), 31-37 https://doi.org/10.1016/0166-8641(96)00009-0
  7. J. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer, Berlin, 1988

Cited by

  1. MINIMAL BASICALLY DISCONNECTED COVERS OF P'-SPACES vol.30, pp.1, 2014, https://doi.org/10.7858/eamj.2014.006
  2. FILTER SPACES AND BASICALLY DISCONNECTED COVERS vol.21, pp.2, 2014, https://doi.org/10.7468/jksmeb.2014.21.2.113