International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 729-734
Atomoicity of mappings
1Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, Wrocław 50-384, Poland
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510, D.F., Mexico
3Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510, D.F., Mexico
Received 16 December 1996; Revised 11 December 1997
Copyright © 1998 Janusz J. Charatonik and Włodzimierz J. Charatonik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
is said to be atomic at a
of the domain
provided that is nondegenerate and . The set
of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all
subcontinua of , is studied. The introduced concept is applied to get new characterizations of atomic
and monotone mappings. Some related questions are asked.