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confluent mapping; quasi-component; connected
Confluence of a mapping between topological spaces can be defined by several ways. J.J. Charatonik asked if two definitions of the confluence using the components and quasi-components are equivalent for surjective mappings with compact point inverses. We give the negative answer to this question in Example 2.1.
[1] Charatonik, J. J.: Mappings related to confluence. Arch. Math. (Brno) 32 (1996), 85 – 103. MR 1407341 | Zbl 0902.54016
[2] Lelek, A., Tymchatyn, E. D.: Pseudo-confluent mappings and classification of continua. Canad. J. Math. 27 (1975), 1336 – 1348. MR 0418022
[3] Steen, L. A., Seebach, J. A. Jr.: Counterexamples in topology. Springer-Verlag, New-York, 1978, pp. . MR 0507446
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