The space of Whitney levels
| Autor: | Alejandro Illanes |
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| Rok vydání: | 1991 |
| Předmět: | |
| Zdroj: | Topology and its Applications. 40:157-169 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/0166-8641(91)90048-q |
| Popis: | Let X be a continuum and let C(X) be the space of subcontinua of X. In this paper we consider the spaces W(X) = {u: C(X)→ R ∣u is a Whitney map and u(X) = 1} with the “sup metric” and, N(X)={u-1(t)∈C(C(X)):u∈ W(X) and 0⩽t⩽1}. We define a natural order for N(X) and we prove that if there is a homeomorphism from N(X) onto N(Y) which preserves order, then X is homeomorphic to Y. Also we prove that W(X) is always homeomorphic to l2 (this answers a question by Nadler). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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