On the domain invariance of countably condensing vector fields (Q555824)
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scientific article; zbMATH DE number 2174924
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the domain invariance of countably condensing vector fields |
scientific article; zbMATH DE number 2174924 |
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On the domain invariance of countably condensing vector fields (English)
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10 June 2005
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It is shown that continuous maps of the form \(\text{ id}-F\) are open if they are locally one-to-one and if \(F\) decreases a measure of noncompactness of countable sets by at least a factor \(k<1\). Actually, the injectivity hypothesis is slightly relaxed. Since the first assumption is satisfied for compact maps, the classical results on the domain invariance of injective functions are a special case.
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domain invariance
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countably condensing map
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measure of noncompactness
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open map
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degree theory
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