Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904025 | Topology and its Applications | 2018 | 15 Pages |
Abstract
Let X and Y be metric continua. We consider the following property (*): if M is a subcontinuum of XÃY such that ÏX(M)=X and ÏY(M)=Y, where ÏX and ÏY are the respective projections on X and Y, then M has small connected neighborhoods in XÃY. Property (*) has been studied by D. P. Bellamy, J. M. Åysko 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 XÃ[0,1] does not have property (*); and (d) the product of a chainable Kelley continuum and [0,1] has property (*).
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Alejandro Illanes, Jorge M. MartÃnez-Montejano, Karen Villarreal,