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RESEARCH PRODUCT
Continuous images of arcs: Extensions of Cornette's Theorem
J. NikielD. DanielL.b. TreybigMurat TuncaliE. D. Tymchatynsubject
Arc (geometry)Discrete mathematicsPure mathematicsCover (topology)Continuum (topology)Images of arcs; Locally connected; Cyclic element; Null familyNull (mathematics)Hausdorff spaceGeometry and TopologyMathematicsImage (mathematics)description
In [J.L. Cornette “Image of a Hausdorff arc” is cyclically extensible and reducible Trans. Am. Math. Soc., 199 (1974), pp. 253–267], Cornette proved that a locally connected Hausdorff continuum X is the continuous image of an arc if and only if each of its cyclic elements is the continuous image of an arc. Cyclic elements form a closed null cover of X by retracts of X. We generalize Cornette's result to closed null covers of X with a dendritic structure. We give examples to show that some of our conditions are necessary and we pose some open questions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-11-01 | Topology and Its Applications |