Atomoicity of Mappings

J. J. Charatonik; W. J. Charatonik

doi:10.1155/S016117129800101X

Atomoicity of Mappings

J. J. Charatonik
, W. J. Charatonik

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	International Journal of Mathematics and Mathematical Sciences
DOIs	https://doi.org/10.1155/S016117129800101X
State	Published - Jan 1 1998

Disciplines

Mathematics
Statistics and Probability

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title = "Atomoicity of Mappings",

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.",

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N2 - 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.

AB - 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.

UR - https://scholarsmine.mst.edu/math_stat_facwork/360

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DO - 10.1155/S016117129800101X

M3 - Article

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

ER -

Atomoicity of Mappings

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