Continuous images of arcs: Extensions of Cornette's Theorem

被引:0
作者
Daniel, D. [1 ]
Nikiel, J. [2 ]
Treybig, L. B. [3 ]
Tuncali, M. [4 ]
Tymchatyn, E. D. [5 ]
机构
[1] Lamar Univ, Dept Math, Beaumont, TX 77710 USA
[2] Opole Univ, Inst Math & Informat, Opole, Poland
[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
[4] Nipissing Univ, Fac Arts & Sci, North Bay, ON P1B 8L7, Canada
[5] Univ Saskatchewan, Dept Math, Saskatoon, SK S7N 0W0, Canada
关键词
Images of arcs; Locally connected; Cyclic element; Null family; HAHN-MAZURKIEWICZ THEOREM; SPACES;
D O I
10.1016/j.topol.2015.09.030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In [2], 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. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:63 / 69
页数:7
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