Geodesic
Partial convexity
Matematičeskie zametki, Tome 60 (1996) no. 3, pp. 406-413.

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We consider a generalization of the classical notion of convexity, which is called partial convexity. Let $V\subseteq\mathbb R^n$ be some set of directions. A set $X\subseteq\mathbb R^n$ is called $V$-convex if the intersection of any line parallel to a vector in $V$ with $X$ is connected. Semispaces and the problem of the least intersection base for partial convexity is investigated. The cone of convexity directions is described for a closed set in $\mathbb R^n$. 
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N. N. Metel'skii; V. N. Martynchik. Partial convexity. Matematičeskie zametki, Tome 60 (1996) no. 3, pp. 406-413. http://geodesic.mathdoc.fr/item/MZM_1996_60_3_a7/

[1] Rawlins G. J. E., Wood D., “Ortho-convexity and its generalizations”, Computational Morphology, ed. G. T. Toussaint, North-Holland, Amsterdam, 1988, 137–152 | MR

[2] Rawlins G. J. E., Wood D., “A decomposition theorem for convexity spaces”, J. Geom., 36 (1989), 143–157 | DOI | MR

[3] Wood D., “An isothetic view of computational geometry”, Computational Geometry, ed. G. T. Toussaint, North-Holland, Amsterdam, 1985, 429–459

[4] Schuierer S., Wood D., Restricted orientation visibility, Report 40, Univ. Freiburg, 1991

[5] Metelskii N. N., Krikun V. S., Izoteticheskie obolochki ogranichennogo ranga, tipa i roda, Preprint in-ta matem. AN BSSR No 10 (410), Minsk, 1990

[6] Metelskii N. N., Krikun V. S., “Razmescheniya izoteticheskikh blokov, optimalnye po obolochechnym kriteriyam”, Dokl. AN SSSR, 317:2 (1991), 320–323 | MR | Zbl

[7] Metelskii N. N., Krikun V. S., Metod ierarkhicheskogo razmescheniya izoteticheskikh blokov, Preprint in-ta matem. AN BSSR No27 (427), Minsk, 1990

[8] Soltan V. P., Vvedenie v aksiomaticheskuyu teoriyu vypuklosti, Shtiintsa, Kishinev, 1984 | Zbl

[9] Klee V. L., “The structure of semispaces”, Math. Scand., 4 (1956), 54–64 | MR | Zbl

[10] Hammer P. C., “Maximal convex sets”, Duke Math. J., 22 (1956), 103–106 | DOI | MR

[11] Hammer P. C., “Semispaces and the topology of convexity”, Convexity, ed. V. L. Klee, AMS Publ., Providence, 1963, 305–316 | MR

[12] Kon P., Universalnaya algebra, Mir, M., 1968

[13] Ore O., Teoriya grafov, Nauka, M., 1980