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Keywords:
continuum; locally connected; open; light; fan; order; component number
continuum; locally connected; open; light; fan; order; component number
Summary:
Whyburn has proved that each open mapping defined on arc (a simple closed curve) is light. Charatonik and Omiljanowski have proved that each open mapping defined on a local dendrite is light. Theorem 3.8 is an extension of these results.
References:
[1] Charatonik J.J., Charatonik W.J., Miklos S.: Confluent mappings of fans. Dissertationes Math. (Rozprawy Mat.) 301 (1990), 1-86. MR 1055706 | Zbl 0776.54025
[2] Charatonik J.J., Omiljanowski K.: On light open mappings. Baku International Topological Conference Proceedings, Baku, 1989, pp. 211-219. MR 1347226 | Zbl 0817.54010
[3] Kuratowski K.: Topology. vol. 2, Academic Press and PWN, 1968. MR 0259836 | Zbl 0849.01044
[4] Maćkowiak T.: Continuous mappings on continua. Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-91. MR 0522934
[5] Menger K.: Kurventheorie. Chelsea Publ. Comp., 1967. MR 0221475 | Zbl 0005.41504
[6] Whyburn G.T.: Analytic topology. Amer. Math. Soc. Colloq. Publ., vol. 28, 1942. MR 0007095 | Zbl 0117.15804
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