Some results on spaces with 1 -calibre

Wei-Feng Xuan; Wei-Xue Shi

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 1, page 131-134
  • ISSN: 0010-2628

Abstract

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We prove that, assuming CH, if X is a space with 1 -calibre and a zeroset diagonal, then X is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular G δ -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with 1 -calibre.

How to cite

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Xuan, Wei-Feng, and Shi, Wei-Xue. "Some results on spaces with $\aleph _1$-calibre." Commentationes Mathematicae Universitatis Carolinae 57.1 (2016): 131-134. <http://eudml.org/doc/276778>.

@article{Xuan2016,
abstract = {We prove that, assuming CH, if $X$ is a space with $\aleph _1$-calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_\delta $-diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with $\aleph _1$-calibre.},
author = {Xuan, Wei-Feng, Shi, Wei-Xue},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\aleph _1$-calibre; star countable; zeroset diagonal},
language = {eng},
number = {1},
pages = {131-134},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some results on spaces with $\aleph _1$-calibre},
url = {http://eudml.org/doc/276778},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Xuan, Wei-Feng
AU - Shi, Wei-Xue
TI - Some results on spaces with $\aleph _1$-calibre
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 1
SP - 131
EP - 134
AB - We prove that, assuming CH, if $X$ is a space with $\aleph _1$-calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_\delta $-diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with $\aleph _1$-calibre.
LA - eng
KW - $\aleph _1$-calibre; star countable; zeroset diagonal
UR - http://eudml.org/doc/276778
ER -

References

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  1. Buzyakova R.Z., Observations on spaces with zeroset or regular G δ -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. MR2174525
  2. Buzyakova R.Z., 10.1016/j.topol.2005.06.004, Topology Appl. 153 (2006), no. 11, 1696–1698. MR2227022DOI10.1016/j.topol.2005.06.004
  3. Basile D., Bella A., Ridderbos G.J., Weak extent, submetrizability and diagonal degrees, Houston J. Math. 40 (2014), no. 1, 255–266. MR3210565
  4. Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  5. Ikenaga S., A class which contains Lindelöf spaces, separable spaces and countably compact spaces, Memoirs of Numazu College of Technology 18 (1983), 105–108. 
  6. Martin H.W., 10.2140/pjm.1975.61.209, Pacific J. Math. 61 (1975), no. 1, 209–217. MR0410685DOI10.2140/pjm.1975.61.209
  7. Wage M.L., Fleissner W.G., Reed G.M., 10.1090/S0002-9904-1976-14150-X, Bull. Amer. Math. Soc. 82 (1976), no. 4, 635–639. MR0410665DOI10.1090/S0002-9904-1976-14150-X
  8. Tall F.D., First Countable Space with 1 -Calibre May or May not be Separable, Set-theoretic Topology, Academic Press, New York, 1977. MR0500795

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