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Open mappings increasing order


Authors: Janusz J. Charatonik and Wlodzimierz J. Charatonik
Journal: Proc. Amer. Math. Soc. 125 (1997), 3725-3733
MSC (1991): Primary 54C10, 54F15; Secondary 54F50
DOI: https://doi.org/10.1090/S0002-9939-97-04096-3
MathSciNet review: 1422853
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Abstract: It is shown that an analog of Whyburn's theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is hereditarily unicoherent.


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Additional Information

Janusz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Address at time of publication: Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: jjc@math.uni.wroc.pl, jjc@gauss.matem.unam.mx

Wlodzimierz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Address at time of publication: Departamento de Matemáticas, Facultad de Ciencias, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: wjcharat@math.uni.wroc.pl, wjcharat@lya.fciencias.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-97-04096-3
Keywords: Classical sense, confluent, continuum, dendroid, light, open mapping, order, smooth
Received by editor(s): May 1, 1996
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society

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