Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 3, page 641-665
  • ISSN: 0392-4041

Abstract

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It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number ω 1 . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly ω 1 . Some classical and recent results are deduced from our criterion.

How to cite

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Ghiloni, Riccardo. "Hausdorff Fréchet closure spaces with maximum topological defect." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 641-665. <http://eudml.org/doc/195263>.

@article{Ghiloni2002,
abstract = {It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number $\omega_\{1\}$. In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly $\omega_\{1\}$. Some classical and recent results are deduced from our criterion.},
author = {Ghiloni, Riccardo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {641-665},
publisher = {Unione Matematica Italiana},
title = {Hausdorff Fréchet closure spaces with maximum topological defect},
url = {http://eudml.org/doc/195263},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Ghiloni, Riccardo
TI - Hausdorff Fréchet closure spaces with maximum topological defect
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 641
EP - 665
AB - It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number $\omega_{1}$. In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly $\omega_{1}$. Some classical and recent results are deduced from our criterion.
LA - eng
UR - http://eudml.org/doc/195263
ER -

References

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  9. FRÉCHET, M., Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo, 22 (1906), 1-74. JFM37.0348.02
  10. GRECO, G. H., The sequential defect of the cross topology is ω 1 , Topology Appl., 19 (1985), 91-94. Zbl0569.54028MR786084
  11. HAUSDORFF, F., Gestufte Raüme, Fundam. Math., 25 (1935), 486-502. Zbl0012.42103
  12. KURATOWSKI, K., Une méthode d'élimination des nombres transfinis des raisonnements mathématiques, Fundam. Math., 3 (1922), 76-108. JFM48.0205.04
  13. NOVÁK, J., On some problems concerning multivalued convergences, Czech. Math. J., 14 (89) (1964), 548-561. Zbl0127.38504MR176439
  14. NOVÁK, J., On convergence spaces and their sequential envelopes, Czech. Math. J., 15 (90) (1965), 74-100. Zbl0139.15906MR175083

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