Article
MSC:
54A10,
54B10,
54B20,
54C65,
54F05 | MR 3478342 | Zbl 06562199 | DOI: 10.14712/1213-7243.2015.147
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Keywords:
hyperspace; Vietoris topology; weak selection; ordinal space
hyperspace; Vietoris topology; weak selection; ordinal space
Summary:
The present paper aims to furnish simple proofs of some recent results about selections on product spaces obtained by García-Ferreira, Miyazaki and Nogura. The topic is discussed in the framework of a result of Katětov about complete normality of products. Also, some applications for products with a countably compact factor are demonstrated as well.
References:
[1] Artico G., Marconi U., Pelant J., Rotter L., Tkachenko M.: Selections and suborderability. Fund. Math. 175 (2002), 1–33. MR 1971236 | Zbl 1019.54014
[2] Buhagiar D., Gutev V.: Selections and countable compactness. Math. Slovaca 63 (2013), no. 5, 1123–1140. DOI 10.2478/s12175-013-0160-z | MR 3122363
[3] Fujii S., Miyazaki K., Nogura T.: Vietoris continuous selections on scattered spaces. J. Math. Soc. Japan 54 (2002), no. 2, 273–281. DOI 10.2969/jmsj/05420273 | MR 1883518
[4] García-Ferreira S., Gutev V., Nogura T., Sanchis M., Tomita A.: Extreme selections for hyperspaces of topological spaces. Topology Appl. 122 (2002), 157–181. DOI 10.1016/S0166-8641(01)00141-9 | MR 1919299
[5] García-Ferreira S., Miyazaki K., Nogura T.: Continuous weak selections for products. Topology Appl. 160 (2013), no. 18, 2465–2472. DOI 10.1016/j.topol.2013.07.040 | MR 3120660
[6] García-Ferreira S., Miyazaki K., Nogura T.: Continuous weak selections and orderability of countable products. preprint, 2013. MR 3120660
[7] García-Ferreira S., Sanchis M.: Weak selections and pseudocompactness. Proc. Amer. Math. Soc. 132 (2004), 1823–1825. DOI 10.1090/S0002-9939-04-06872-8 | MR 2051146
[8] Glicksberg I.: Stone-Čech compactifications of products. Trans. Amer. Math. Soc. 90 (1959), 369–382. MR 0105667 | Zbl 0089.38702
[9] Gutev V.: Selections and hyperspaces. Recent progress in general topology, III (K.P. Hart, J. van Mill, and P. Simon, eds.), Atlantis Press, Springer, 2014, pp. 535–579. MR 3205492
[10] Gutev V., Nogura T.: Selections and order-like relations. Appl. Gen. Topol. 2 (2001), 205–218. MR 1890037
[11] Gutev V., Nogura T.: Selection pointwise-maximal spaces. Topology Appl. 146–147 (2005), 397–408. MR 2107159
[12] Hewitt E.: Rings of real-valued continuous functions. I. Trans. Amer. Math. Soc. 64 (1948), 45–99. DOI 10.1090/S0002-9947-1948-0026239-9 | MR 0026239
[13] Katětov M.: Complete normality of Cartesian products. Fund. Math. 35 (1948), 271–274. MR 0027501
[14] Michael E.A.: Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71 (1951), 152–182. DOI 10.1090/S0002-9947-1951-0042109-4 | MR 0042109 | Zbl 0043.37902
[15] van Mill J., Wattel E.: Selections and orderability. Proc. Amer. Math. Soc. 83 (1981), no. 3, 601–605. DOI 10.1090/S0002-9939-1981-0627702-4 | MR 0627702
[16] Miyazaki K.: Continuous selections on almost compact spaces. Sci. Math. Jpn. 53 (2001), 489–494. MR 1835918
[17] Treybig L.B.: Concerning continuous images of compact ordered spaces. Proc. Amer. Math. Soc. 15 (1964), 866–871. DOI 10.1090/S0002-9939-1964-0167953-9 | MR 0167953
[18] van Douwen E.K.: Mappings from hyperspaces and convergent sequences. Topology Appl. 34 (1990), 35–45. DOI 10.1016/0166-8641(90)90087-I | MR 1035458
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