Document Type

Article

Language

eng

Format of Original

12 p.

Publication Date

2009

Publisher

University of Houston

Source Publication

Houston Journal of Mathematics

Source ISSN

0362-1588

Abstract

For each positive ordinal α, the reflexive and transitive binary relation of α-dominance between compacta was first defined in our paper [Mapping properties of co-existentially closed continua, Houston J. Math., 31 (2005), 1047-1063] using the ultracopower construction. Here we consider the important special case α =2, and show that any Peano compactum 2-dominated by a dendrite is itself a dendrite (with the same being true for topological graphs and trees). We also characterize the topological graphs that 2-dominate arcs (resp., simple closed curves) as those that have cut points of order 2 (resp., those that are not trees).

Comments

Published version. Houston Journal of Mathematics, Vol. 35, No. 4 (2009): 1091-1102. Publisher Link. © 2009 University of Houston. Used with permission.

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