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

来源：

TOPOLOGY AND ITS APPLICATIONS | 2015年 / 195卷

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

页码：63 / 69

页数：7

共 17 条

[1] A CHARACTERIZATION OF CONTINUOUS IMAGES OF COMPACT ORDERED SPACES AND THE HAHN-MAZURKIEWICZ PROBLEM [J].