We study monotone path-connected sets and also strongly and weakly Menger-connected sets. We introduce the notion of -solarity and establish a connection with the notion of solarity. We prove that boundedly compact suns in are monotone path-connected.

中文翻译：

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单调路径连通集的性质

我们研究单调路径连接集以及强和弱门格尔连接集。我们引入-solarity 的概念，并与solarity 的概念建立联系。我们证明了有界紧致的太阳是单调路径连通的。