Connected neighborhoods in products
Por:
Illanes, Alejandro, Martinez-Montejano, Jorge M., Villarreal, Karen
Publicada:
1 jun 2018
Categoría:
Geometry and topology
Resumen:
Let X and Y be metric continua. We consider the following property (*): if M is a subcontinuum of X×Y such that pX(M)=X and pY(M)=Y, where pX and pY are the respective projections on X and Y, then M has small connected neighborhoods in X×Y. Property (*) has been studied by D. P. Bellamy, J. M. Lysko and the first named author. In this paper we continue studying property (*) in products of continua. We prove: (a) the product of homogeneous continua having the fixed point property has property (*); (b) the product of a solenoid and any Knaster continuum has property (*); (c) there exists a Kelley continuum X such that X×[0,1] does not have property (*); and (d) the product of a chainable Kelley continuum and [0,1] has property (*). © 2018 Elsevier B.V.
Filiaciones:
Illanes, Alejandro:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, D.F., Mexico
Univ Nacl Autonoma Mexico, Inst Matemat, Cd Univ, Mexico City 04510, DF, Mexico
Martinez-Montejano, Jorge M.:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, D.F., Mexico
Univ Nacl Autonoma Mexico, Dept Matemat, Fac Ciencias, Cd Univ, Mexico City 04510, DF, Mexico
Villarreal, Karen:
Department of Mathematical Sciences, Loyola University, New Orleans, LA, United States
Loyola Univ, Dept Math Sci, New Orleans, LA 70118 USA
|