Atomicity of mappings (Q1273333)
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scientific article; zbMATH DE number 1230049
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Atomicity of mappings |
scientific article; zbMATH DE number 1230049 |
Statements
Atomicity of mappings (English)
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6 December 1998
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Summary: A mapping \(f:X\to Y\) between continua \(X\) and \(Y\) is said to be atomic at a subcontinuum \(K\) 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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composition factor property
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contratomic
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atomic at a subcontinuum
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hyperspace of all subcontinua
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monotone mappings
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