| Title:
|
Remarks on cardinal inequalities in convergence spaces (English) |
| Author:
|
Yoshitomi, Kazushi |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
215-227 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
convergence space |
| Keyword:
|
cardinal function |
| Keyword:
|
inequality |
| Keyword:
|
set-theoretic topology |
| MSC:
|
54A20 |
| MSC:
|
54A25 |
| DOI:
|
10.21136/MB.2020.0090-19 |
| . |
| Date available:
|
2021-05-20T13:55:34Z |
| Last updated:
|
2021-06-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148933 |
| . |
| Reference:
|
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| Reference:
|
[2] Čech, E.: Topological Spaces.Publishing House of the Czechoslovak Academy of Sciences, Prague; John Wiley & Sons, London (1966). Zbl 0141.39401, MR 0211373 |
| Reference:
|
[3] Choquet, G.: Convergences.Ann. Univ. Grenoble, Sect. Sci. Math. Phys., II. Ser. 23 (1948), 57-112. Zbl 0031.28101, MR 0025716 |
| Reference:
|
[4] Dolecki, S., Gauld, D.: Irregularity.Topology Appl. 154 (2007), 1565-1580 Erratum ibid. 159 2012 3658-3659. Zbl 1119.54002, MR 2317063, 10.1016/j.topol.2006.11.009 |
| Reference:
|
[5] Dolecki, S., Mynard, F.: Convergence Foundations of Topology.World Scientific, Hackensack (2016). Zbl 1345.54001, MR 3497013, 10.1142/9012 |
| Reference:
|
[6] Katětov, M.: Über $H$-abgeschlossene und bikompakte Räume.Čas. Pěst. Mat. Fys. 69 (1940), 36-49 German. Zbl 0022.41203, MR 0001912, 10.21136/CPMF.1940.121983 |
| Reference:
|
[7] Katětov, M.: On $H$-closed extensions of topological spaces.Čas. Pěst. Mat. Fys. 72 (1947), 17-32. Zbl 0041.51504, MR 0022069, 10.21136/CPMF.1947.109025 |
| Reference:
|
[8] Reynolds, J. P.: Hausdorff closedness in the convergence setting.Topol. Proc. 49 (2017), 135-152. Zbl 1373.54006, MR 3546386 |
| Reference:
|
[9] Rudin, M. E.: Lectures on Set Theoretic Topology.CBMS Regional Conference Series in Mathematics 23. AMS, Providence (1975). Zbl 0318.54001, MR 0367886, 10.1090/cbms/023 |
| . |
