Geodesic
On monotone orthocompactness
Serdica Mathematical Journal, Tome 44 (2018) no. 1-2, pp. 177-186.

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Junnila and Künzi defined monotone orthocompactness via transitive neighbornets, and proved that monotonically normal, monotonically orthocompact spaces must have an ortho-base. Answering one of Junnila and Künzi’s questions, Shouli and Yuming claimed to have provided an example of a monotonically orthocompact space without an ortho-base. We define a version of monotone orthocompactness via interior-preserving open refinements and show that it is a strictly weaker property than monotone orthocompactness of Junnila and Künzi, and we point out an error in the paper by Shouli and Yuming, thereby indicating that the question of Junnila and Künzi appears to remain open.
Keywords: monotone covering properties, monotonically orthocompact, orthobase, transitive neighbornet, GO-space, regressive functions on ω1, NSR base, 54D20, 54D70, 54F05, 54B10, 54G20, 54D65 
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Popvassilev, Strashimir G.; Porter, John E. On monotone orthocompactness. Serdica Mathematical Journal, Tome 44 (2018) no. 1-2, pp. 177-186. http://geodesic.mathdoc.fr/item/SMJ2_2018_44_1-2_a8/