Free Cells in Hyperspaces of Graphs

José Ángel Juárez Morales, Gerardo Reyna Hernández, Jesús Romero Valencia and Omar Rosario Cayetano
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José Ángel Juárez Morales: Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 54, Col. La Garita, Acapulco 39650, Guerrero, Mexico
Gerardo Reyna Hernández: Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 54, Col. La Garita, Acapulco 39650, Guerrero, Mexico
Jesús Romero Valencia: Faculty of Mathematics, Autonomous University of Guerrero, Sauce 19, La Cima, Chilpancingo de los Bravo 39086, Guerrero, Mexico
Omar Rosario Cayetano: Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 54, Col. La Garita, Acapulco 39650, Guerrero, Mexico

Mathematics, 2021, vol. 9, issue 14, 1-11

Abstract: Often for understanding a structure, other closely related structures with the former are associated. An example of this is the study of hyperspaces. In this paper, we give necessary and sufficient conditions for the existence of finitely-dimensional maximal free cells in the hyperspace C ( G ) of a dendrite G ; then, we give necessary and sufficient conditions so that the aforementioned result can be applied when G is a dendroid. Furthermore, we prove that the arc is the unique arcwise connected, compact, and metric space X for which the anchored hyperspace C p ( X ) is an arc for some p ? X .

Keywords: hyperspace; graph; dendroid; dendrite (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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