Geodesic
Concerning Upper Semi-Continuous Decompositions of En Whose Non-Degenerate Elements are Polyhedral Arcs or Star-Like Continua
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1308-1314

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In (1) Armentrout raised the question “Is there a monotone decomposition of E3 into arcs?” The analogous question for E2 was answered negatively by Roberts in (8). Our aim in this paper is to give a partial answer to Armentrout's question by proving the following theorem. 
Treybig, L. B. Concerning Upper Semi-Continuous Decompositions of En Whose Non-Degenerate Elements are Polyhedral Arcs or Star-Like Continua. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1308-1314. doi: 10.4153/CJM-1968-129-3
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[1] 1. Armentrout, Steve, Monotone decompositions of E's, Annals of Math. Studies, No. 60, pp. 1–25 (Princeton Univ. Press, Princeton, N.J., 1966). Google Scholar

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