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.
J. J. Charatonik and W. J. Charatonik, "Atomoicity of Mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi Publishing Corporation, Jan 1998.
The definitive version is available at https://doi.org/10.1155/S016117129800101X
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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