Previous |  Up |  Next

Article

Keywords:
stratifiable space; $\varkappa $-metrizable space; Niemytzki plane; Sorgenfrey line
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.
References:
[1] Bielas, W., Plewik, Sz.: On $RC$-spaces. Arab. J. Math. 9 (2020), 83-88. DOI 10.1007/s40065-018-0233-5 | MR 4062894 | Zbl 1435.54008
[2] Borges, C. J. R.: On stratifiable spaces. Pac. J. Math. 17 (1966), 1-16. DOI 10.2140/pjm.1966.17.1 | MR 0188982 | Zbl 0175.19802
[3] Ceder, J. G.: Some generalizations of metric spaces. Pac. J. Math. 11 (1961), 105-125. DOI 10.2140/pjm.1961.11.105 | MR 0131860 | Zbl 0103.39101
[4] Chigogidze, A. Ch.: On $\kappa$-metrizable spaces. Russ. Math. Surv. 37 (1982), 209-210 translation from Uspekhi Mat. Nauk 37 1982 241-242. DOI 10.1070/RM1982v037n02ABEH003916 | MR 0650791 | Zbl 0503.54012
[5] Engelking, R.: General Topology. Sigma Series in Pure Mathematics 6. Heldermann Verlag, Berlin (1989). MR 1039321 | Zbl 0684.54001
[6] Kalantan, L.: Results about $\kappa$-normality. Topology Appl. 125 (2002), 47-62. DOI 10.1016/S0166-8641(01)00258-9 | MR 1931174 | Zbl 1026.54014
[7] Kalemba, P., Plewik, Sz.: On regular but not completely regular spaces. Topology Appl. 252 (2019), 191-197. DOI 10.1016/j.topol.2018.11.006 | MR 3884192 | Zbl 1407.54014
[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. DOI 10.1070/RM1976v031n05ABEH004195 | MR 0464137 | Zbl 0356.54026
[9] Shchepin, E. V.: On $\kappa$-metrizable spaces. Izv. Akad. Nauk SSSR, Ser. Mat. 43 (1979), 442-478 Russian. MR 0534603 | Zbl 0409.54040
[10] Sierpiński, W.: Introduction to General Topology. University of Toronto Press, Toronto (1934). Zbl 0009.23203
[11] L. A. Steen, J. A. Seebach, Jr.: Counterexamples in Topology. Holt, Rinehart and Winston, New York (1970). MR 0266131 | Zbl 0211.54401
[12] Suzuki, J., Tamano, K., Tanaka, Y.: $\kappa$-metrizable spaces, stratifiable spaces and metrization. Proc. Am. Math. Soc. 105 (1989), 500-509. DOI 10.1090/S0002-9939-1989-0933521-9 | MR 0933521 | Zbl 0672.54021
Partner of
EuDML logo