A note on D-spaces

Shou Lin

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 2, page 313-316
  • ISSN: 0010-2628

Abstract

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Every semi-stratifiable space or strong Σ -space has a σ -cushioned (mod k )-network. In this paper it is showed that every space with a σ -cushioned (mod k )-network is a D-space, which is a common generalization of some results about D-spaces.

How to cite

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Lin, Shou. "A note on D-spaces." Commentationes Mathematicae Universitatis Carolinae 47.2 (2006): 313-316. <http://eudml.org/doc/249870>.

@article{Lin2006,
abstract = {Every semi-stratifiable space or strong $\Sigma $-space has a $\sigma $-cushioned (mod$k$)-network. In this paper it is showed that every space with a $\sigma $-cushioned (mod$k$)-network is a D-space, which is a common generalization of some results about D-spaces.},
author = {Lin, Shou},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {D-spaces; (mod$k$)-networks; cushioned collections; semi-stratifiable spaces; D-spaces; (mod )-networks; cushioned collections; semi-stratifiable spaces},
language = {eng},
number = {2},
pages = {313-316},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on D-spaces},
url = {http://eudml.org/doc/249870},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Lin, Shou
TI - A note on D-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 2
SP - 313
EP - 316
AB - Every semi-stratifiable space or strong $\Sigma $-space has a $\sigma $-cushioned (mod$k$)-network. In this paper it is showed that every space with a $\sigma $-cushioned (mod$k$)-network is a D-space, which is a common generalization of some results about D-spaces.
LA - eng
KW - D-spaces; (mod$k$)-networks; cushioned collections; semi-stratifiable spaces; D-spaces; (mod )-networks; cushioned collections; semi-stratifiable spaces
UR - http://eudml.org/doc/249870
ER -

References

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  1. Arhangel'skii A.V., Buzyakova R.Z., Addition theorems and D-spaces, Comment. Math. Univ. Carolin. 43 (2002), 653-663. (2002) Zbl1090.54017MR2045787
  2. Borges C.R., Wehrly A.C., A study of D-spaces, Topology Proc. 16 (1991), 7-15. (1991) Zbl0787.54023MR1206448
  3. Buzyakova R.Z., On D-property of strong Σ -spaces, Comment. Math. Univ. Carolin. 43 (2002), 493-495. (2002) Zbl1090.54018MR1920524
  4. Creede G., Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47-54. (1970) Zbl0189.23304MR0254799
  5. van Douwen E.K., Simultaneous extension of continuous functions, Thesis, Free University, Amsterdam, 1975. 
  6. van Douwen E.K., Pfeffer W.F., Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (1979), 371-377. (1979) Zbl0409.54011MR0547605
  7. Engelking R., General Topology (Revised and completed edition), Heldermann Verlag, Berlin, 1989. MR1039321
  8. Gruenhage G., Generalized metric spaces, in Handbook of Set-Theoretic Topology, K. Kunen, J.E. Vaughan (Eds.), Elsevier Science Publishers B.V., Amsterdam, 1984, pp.423-501. Zbl0794.54034MR0776629

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