Abstract Given a family of metric continua { X α : α ∈ J } , we consider the following property for the product X = ∏ α ∈ J X α : 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. Martinez-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.

中文翻译：

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两个可链接的 Kelley 连续体的乘积具有 fupcon 性质

摘要 给定一族度量连续体 { X α : α ∈ J } ，我们考虑乘积 X = ∏ α ∈ JX α 的以下性质：如果 M 是投影到每个因子空间的 X 的子连续体，则 M 具有任意小连接的开放社区。此属性被称为 fupcon（完​​整投影意味着连接的开放社区）属性，并且已被多位作者研究过。特别是在 2018 年，A. Illanes、JM Martinez-Montejano 和 K. Villarreal 证明了可链接的 Kelley 连续统与 [0,1] 的乘积具有 fupcon 性质。在本文中，我们通过证明两个可链接的 Kelley 连续体的乘积具有 fupcon 性质来扩展该结果。