Abstract
Given a family of metric continua {Xα:α∈J}, we consider the following property for the product X=∏α∈JXα: if M is a subcontinuum of X projecting onto each factor space, then M has arbitrarily small connected open neighborhoods. This property has been called fupcon (full projections imply connected open neighborhoods) property and it has been studied by several authors. Particularly, in 2018, A. Illanes, J. M. Martínez-Montejano and K. Villarreal proved that the product of a chainable Kelley continuum and [0,1] has the fupcon property. In this paper, we extend this result by proving that the product of two chainable Kelley continua has the fupcon property.
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