Geodesic
Properties of monotone path-connected sets
Izvestiya. Mathematics , Tome 85 (2021) no. 2, pp. 306-331.

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We study monotone path-connected sets and also strongly and weakly Menger-connected sets. We introduce the notion of $\varepsilon$-solarity and establish a connection with the notion of solarity. We prove that boundedly compact suns in $C(Q)$ are monotone path-connected.
Keywords: spans, monotone path-connected sets, Menger connectedness, solarity. 
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I. G. Tsar'kov. Properties of monotone path-connected sets. Izvestiya. Mathematics , Tome 85 (2021) no. 2, pp. 306-331. http://geodesic.mathdoc.fr/item/IM2_2021_85_2_a5/

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