Observations on spaces with zeroset or regular G δ -diagonals

Raushan Z. Buzyakova

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 469-473
  • ISSN: 0010-2628

Abstract

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We show that if X 2 has countable extent and X has a zeroset diagonal then X is submetrizable. We also make a couple of observations regarding spaces with a regular G δ -diagonal.

How to cite

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Buzyakova, Raushan Z.. "Observations on spaces with zeroset or regular $G_\delta $-diagonals." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 469-473. <http://eudml.org/doc/249521>.

@article{Buzyakova2005,
abstract = {We show that if $X^2$ has countable extent and $X$ has a zeroset diagonal then $X$ is submetrizable. We also make a couple of observations regarding spaces with a regular $G_\delta $-diagonal.},
author = {Buzyakova, Raushan Z.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {zeroset diagonal; regular $G_\delta $-diagonal; submetrizable; countable extent; submetrizable; countable extent},
language = {eng},
number = {3},
pages = {469-473},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Observations on spaces with zeroset or regular $G_\delta $-diagonals},
url = {http://eudml.org/doc/249521},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Buzyakova, Raushan Z.
TI - Observations on spaces with zeroset or regular $G_\delta $-diagonals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 469
EP - 473
AB - We show that if $X^2$ has countable extent and $X$ has a zeroset diagonal then $X$ is submetrizable. We also make a couple of observations regarding spaces with a regular $G_\delta $-diagonal.
LA - eng
KW - zeroset diagonal; regular $G_\delta $-diagonal; submetrizable; countable extent; submetrizable; countable extent
UR - http://eudml.org/doc/249521
ER -

References

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  1. Arhangelskii A.V., On a class of spaces containing all metric spaces and all locally compact spaces, Mat. Sb 67 (1965), English Translation: Amer. Math. Soc. Transl. 92 (1970), 1-39. (1970) MR0190889
  2. Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl0684.54001MR1039321
  3. Fleissner W.G., Reed G.M., Wage M.L., Normality versus countable paracompactness in perfect spaces, Bull. Amer. Math. Soc. 82 4 (1976), 635-639. (1976) Zbl0332.54018MR0410665
  4. Karpov A.N., Countable products of Čech-complete linearly Lindelöf and initially-compact spaces, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (2000), 5 7-9, 67. (2000) Zbl0984.54006MR1799346
  5. Martin H.W., Contractibility of topological spaces onto metric spaces, Pacific J. Math. 61 (1975), 1 209-217. (1975) Zbl0304.54026MR0410685

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