Approximation of Dendroids by Trees

Robert Cauty; W. J. Charatonik; Jennifer Smith

Approximation of Dendroids by Trees

Robert Cauty
, W. J. Charatonik
, Jennifer Smith

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that, for every dendroid X, every tree To contained in X and every e > 0, there exists a tree T, contained in X and containing To and an epslion-retraction of X onto T. This implies that every dendroid is the limit of a projective sequence formed of trees and retractions.

Original language	American English
Journal	Analysis and Topology
State	Published - Jan 1 2008

Disciplines

Mathematics
Statistics and Probability

Cite this

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title = "Approximation of Dendroids by Trees",

abstract = " We prove that, for every dendroid X, every tree To contained in X and every e > 0, there exists a tree T, contained in X and containing To and an epslion-retraction of X onto T. This implies that every dendroid is the limit of a projective sequence formed of trees and retractions.",

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AU - Cauty, Robert

AU - Charatonik, W. J.

AU - Smith, Jennifer

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N2 - We prove that, for every dendroid X, every tree To contained in X and every e > 0, there exists a tree T, contained in X and containing To and an epslion-retraction of X onto T. This implies that every dendroid is the limit of a projective sequence formed of trees and retractions.

AB - We prove that, for every dendroid X, every tree To contained in X and every e > 0, there exists a tree T, contained in X and containing To and an epslion-retraction of X onto T. This implies that every dendroid is the limit of a projective sequence formed of trees and retractions.

UR - https://scholarsmine.mst.edu/math_stat_facwork/190

M3 - Article

JO - Analysis and Topology

JF - Analysis and Topology

ER -

Approximation of Dendroids by Trees

Abstract

Disciplines

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