Geodesic
Spiral connectedness of the sections and projections of $\mathbb C$-convex sets
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 359-369.

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The notion of structural dimension of $\mathbb C$-convex sets is introduced. The spiral connectedness of sections and projections of these sets, as well as of the complements of these sections and projections is established. Examples refining L. A. Aizenberg's well-known conjecture about the approximation of strongly linearly convex sets are presented. 
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S. V. Znamenskii; L. N. Znamenskaya. Spiral connectedness of the sections and projections of $\mathbb C$-convex sets. Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 359-369. http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a4/

[1] Martineau A., “Sur la notion d'ensemble fortement linéelement convexe”, Anais. Acad. Brasil. Ciènc., 4:4 (1968), 427–435 | MR

[2] Znamenskii S. V., “Silnaya lineinaya vypuklost”, Kompleksnyi analiz i matematicheskaya fizika, In-t fiziki im. L. V. Kirenskogo SO AN SSSR, Krasnoyarsk, 1988, 39–52 | MR

[3] Znamenskii S. V., “Tomografiya v prostranstvakh analiticheskikh funktsionalov”, Dokl. AN SSSR, 312:5 (1990), 1037–1040 | MR | Zbl

[4] Andersson M., Passare M., “Complex Kergin interpolation”, J. Approxim. Theory, 64:2 (1991), 214–225 | DOI | MR | Zbl

[5] Znamenskii S. V., “Silnaya lineinaya vypuklost. I: Dvoistvennost prostranstv golomorfnykh funktsii”, Sib. matem. zh., 26:3 (1985), 32–43 | MR

[6] Znamenskii S. V., “Geometricheskii kriterii silnoi lineinoi vypuklosti”, Funktsion. analiz i ego prilozh., 13:3 (1979), 83–84 | MR | Zbl

[7] Zelinskii Yu. B., “O geometricheskikh kriteriyakh silnoi lineinoi vypuklosti”, Dokl. AN SSSR, 261:1 (1981), 11–13 | MR | Zbl

[8] Andersson M., “Cauchy–Fantappiè–Leray formulas with local sections and the inverse Fantappiè transform”, Bull. Soc. Math. France, 120 (1992), 113–128 | MR | Zbl

[9] Yuzhakov A. P., Krivokolesko V. P., “Nekotorye svoistva lineino vypuklykh oblastei s gladkimi granitsami v $\mathbb C^n$”, Sib. matem. zh., 1971, no. 2, 452–458 | Zbl

[10] Znamenskii S. V., “Primer silno lineino vypukloi oblasti s nespryamlyaemoi granitsei”, Matem. zametki, 57:6 (1994), 851–861 | MR

[11] Aizenberg L. A., “Lineinye funktsionaly v prostranstvakh analiticheskikh funktsii i lineinaya vypuklost v $\mathbb C^n$”, Issledovaniya po lineinym operatoram i teorii funktsii. 99 nereshennykh zadach lineinogo i kompleksnogo analiza, Zapiski nauchnykh seminarov LOMI, 81, Nauka, L., 1978, 29–32

[12] Engelking R., Obschaya topologiya, Mir, M., 1986

[13] Kuratovskii K., Topologiya, T. 2, Mir, M., 1969