Remarks on cardinal inequalities in convergence spaces

Kazushi Yoshitomi

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 2, page 215-227
  • ISSN: 0862-7959

Abstract

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We extend the Noble and Ulmer theorem and the Juhász and Hajnal theorems in set-theoretic topology. We show that a statement analogous to that in the former theorem is valid for a family of almost topological convergences, whereas statements analogous to those in the latter theorems hold for a pretopologically Hausdorff convergence.

How to cite

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Yoshitomi, Kazushi. "Remarks on cardinal inequalities in convergence spaces." Mathematica Bohemica 146.2 (2021): 215-227. <http://eudml.org/doc/297707>.

@article{Yoshitomi2021,
abstract = {We extend the Noble and Ulmer theorem and the Juhász and Hajnal theorems in set-theoretic topology. We show that a statement analogous to that in the former theorem is valid for a family of almost topological convergences, whereas statements analogous to those in the latter theorems hold for a pretopologically Hausdorff convergence.},
author = {Yoshitomi, Kazushi},
journal = {Mathematica Bohemica},
keywords = {convergence space; cardinal function; inequality; set-theoretic topology},
language = {eng},
number = {2},
pages = {215-227},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on cardinal inequalities in convergence spaces},
url = {http://eudml.org/doc/297707},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Yoshitomi, Kazushi
TI - Remarks on cardinal inequalities in convergence spaces
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 2
SP - 215
EP - 227
AB - We extend the Noble and Ulmer theorem and the Juhász and Hajnal theorems in set-theoretic topology. We show that a statement analogous to that in the former theorem is valid for a family of almost topological convergences, whereas statements analogous to those in the latter theorems hold for a pretopologically Hausdorff convergence.
LA - eng
KW - convergence space; cardinal function; inequality; set-theoretic topology
UR - http://eudml.org/doc/297707
ER -

References

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  7. Katětov, M., 10.21136/CPMF.1947.109025, Čas. Pěst. Mat. Fys. 72 (1947), 17-32. (1947) Zbl0041.51504MR0022069DOI10.21136/CPMF.1947.109025
  8. Reynolds, J. P., Hausdorff closedness in the convergence setting, Topol. Proc. 49 (2017), 135-152. (2017) Zbl1373.54006MR3546386
  9. Rudin, M. E., 10.1090/cbms/023, CBMS Regional Conference Series in Mathematics 23. AMS, Providence (1975). (1975) Zbl0318.54001MR0367886DOI10.1090/cbms/023

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