International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 729-734
doi:10.1155/S016117129800101X
Atomicity of mappings
Janusz J. Charatonik
and Włodzimierz J. Charatonik
Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, Wrocław 50-384, Poland
Abstract
A mapping f:X→Y between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f−1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.