The fixed-point property under induced interval maps of continua
Let f : I → I be a continuous map of a compact interval I and C(I) be the hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We investigate the existence of the fixed-point property of subsets of C(I) with respect to any induced interval map F : C(I) → C(I). In particula...
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| Date: | 2015 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2015
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/177135 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The fixed-point property under induced interval maps of continua / D. Robatian // Нелінійні коливання. — 2015. — Т. 18, № 1. — С. 102-111 — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Let f : I → I be a continuous map of a compact interval I and C(I) be the hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We investigate the existence of the fixed-point property of subsets of C(I) with respect to any induced interval map F : C(I) → C(I). In particular, we prove that any nonempty subcontinuum of C(I) has the fixed-point property. |
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