Whitney preserving maps on finite graphs
| Autor: | Alejandro Illanes, Benjamin Espinoza |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Whitney conditions Hyperspace Whitney map Mathematics::General Topology Finite graph Locally connected continuum Whitney preserving map Mathematics::Geometric Topology Whitney levels Jordan curve theorem Graph Homeomorphism Combinatorics symbols.namesake Unit circle Arcwise connected symbols Continuum Arcwise connected continuum Weakly confluent map Geometry and Topology Mathematics |
| Zdroj: | Topology and its Applications. 158(8):1033-1044 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2011.02.010 |
| Popis: | For a Whitney preserving map f : X → G we show the following: (a) If X is arcwise connected and G is a graph which is not a simple closed curve, then f is a homeomorphism; (b) If X is locally connected and G is a simple closed curve, then X is homeomorphic to either the unit interval [ 0 , 1 ] , or the unit circle S 1 . As a consequence of these results, we characterize all Whitney preserving maps between finite graphs. We also show that every hereditarily weakly confluent Whitney preserving map between locally connected continua is a homeomorphism. |
| Databáze: | OpenAIRE |
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