| Title:
|
The Niemytzki plane is $\varkappa $-metrizable (English) |
| Author:
|
Bielas, Wojciech |
| Author:
|
Kucharski, Andrzej |
| Author:
|
Plewik, Szymon |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
457-469 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the Niemytzki plane is $\varkappa $-metrizable and we try to explain the differences between the concepts of a stratifiable space and a $\varkappa $-metrizable space. Also, we give a characterisation of $\varkappa $-metrizable spaces which is modelled on the version described by Chigogidze. (English) |
| Keyword:
|
stratifiable space |
| Keyword:
|
$\varkappa $-metrizable space |
| Keyword:
|
Niemytzki plane |
| Keyword:
|
Sorgenfrey line |
| MSC:
|
54D15 |
| MSC:
|
54E35 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 07442513 |
| idMR:
|
MR4336550 |
| DOI:
|
10.21136/MB.2021.0177-19 |
| . |
| Date available:
|
2021-11-08T16:21:02Z |
| Last updated:
|
2021-12-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149260 |
| . |
| Reference:
|
[1] Bielas, W., Plewik, Sz.: On $RC$-spaces.Arab. J. Math. 9 (2020), 83-88. Zbl 1435.54008, MR 4062894, 10.1007/s40065-018-0233-5 |
| Reference:
|
[2] Borges, C. J. R.: On stratifiable spaces.Pac. J. Math. 17 (1966), 1-16. Zbl 0175.19802, MR 0188982, 10.2140/pjm.1966.17.1 |
| Reference:
|
[3] Ceder, J. G.: Some generalizations of metric spaces.Pac. J. Math. 11 (1961), 105-125. Zbl 0103.39101, MR 0131860, 10.2140/pjm.1961.11.105 |
| Reference:
|
[4] Chigogidze, A. Ch.: On $\kappa$-metrizable spaces.Russ. Math. Surv. 37 (1982), 209-210 translation from Uspekhi Mat. Nauk 37 1982 241-242. Zbl 0503.54012, MR 0650791, 10.1070/RM1982v037n02ABEH003916 |
| Reference:
|
[5] Engelking, R.: General Topology.Sigma Series in Pure Mathematics 6. Heldermann Verlag, Berlin (1989). Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] Kalantan, L.: Results about $\kappa$-normality.Topology Appl. 125 (2002), 47-62. Zbl 1026.54014, MR 1931174, 10.1016/S0166-8641(01)00258-9 |
| Reference:
|
[7] Kalemba, P., Plewik, Sz.: On regular but not completely regular spaces.Topology Appl. 252 (2019), 191-197. Zbl 1407.54014, MR 3884192, 10.1016/j.topol.2018.11.006 |
| Reference:
|
[8] Shchepin, E. V.: Topology of limit spaces with uncountable inverse spectra.Russ. Math. Surv. 31 (1976), 155-191 translation from Uspekhi Mat. Nauk 31 1976 191-226. Zbl 0356.54026, MR 0464137, 10.1070/RM1976v031n05ABEH004195 |
| Reference:
|
[9] Shchepin, E. V.: On $\kappa$-metrizable spaces.Izv. Akad. Nauk SSSR, Ser. Mat. 43 (1979), 442-478 Russian. Zbl 0409.54040, MR 0534603 |
| Reference:
|
[10] Sierpiński, W.: Introduction to General Topology.University of Toronto Press, Toronto (1934). Zbl 0009.23203 |
| Reference:
|
[11] L. A. Steen, J. A. Seebach, Jr.: Counterexamples in Topology.Holt, Rinehart and Winston, New York (1970). Zbl 0211.54401, MR 0266131 |
| Reference:
|
[12] Suzuki, J., Tamano, K., Tanaka, Y.: $\kappa$-metrizable spaces, stratifiable spaces and metrization.Proc. Am. Math. Soc. 105 (1989), 500-509. Zbl 0672.54021, MR 0933521, 10.1090/S0002-9939-1989-0933521-9 |
| . |
