On the connectivity properties of the solution set of parametrized families of compact vector fields (Q1056896)
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scientific article; zbMATH DE number 3895732
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the connectivity properties of the solution set of parametrized families of compact vector fields |
scientific article; zbMATH DE number 3895732 |
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On the connectivity properties of the solution set of parametrized families of compact vector fields (English)
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1984
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An extension to n-parameter families of compact vector fields of the well-known Leray-Schauder continuation principle is obtained. Using Čech cohomology, it is proved that (under the usual assumptions) the zero-set of the family contains a closed connected subset of dimension at least n whose projection covers all of the parameters space. See also [\textit{P. M. Fitzpatrick} and the authors Math. Ann. 263, 61-73 (1983; Zbl 0519.58024)].
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n-parameter families of compact vector fields
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Leray-Schauder continuation principle
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Čech cohomology
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zero-set
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