Geodesic
On acyclicity of the set of solutions to the Cauchy problem for differential equations
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 836-842.

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The acyclicity of sets of solutions to the Cauchy problem is considered from the viewpoint of the axiomatic theory of solutions spaces of ordinary differential equations. We prove that the class of acyclic solution spaces is closed with respect to passing to the limit space. 
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B. S. Klebanov; V. V. Filippov. On acyclicity of the set of solutions to the Cauchy problem for differential equations. Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 836-842. http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a4/

[1] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, Izd-vo MGU, M., 1988 | Zbl

[2] Filippov V. V., “Topologicheskoe stroenie prostranstv reshenii obyknovennykh differentsialnykh uravnenii”, UMN, 48:1 (1993), 103–154 | MR | Zbl

[3] Filippov V. V., Prostranstva reshenii obyknovennykh differentsialnykh uravnenii, Izd-vo MGU, M., 1993 | Zbl

[4] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | Zbl

[5] Klebanov B. S., “On Wa. zewski's topological principle”, Interim Report of the Prague Topological Symposium, Prague, 1987, 29

[6] Filippov V. V., O suschestvovanii periodicheskikh reshenii, Preprint, MGU, M., 1994

[7] Stinrod N., Eilenberg S., Osnovaniya algebraicheskoi topologii, Fizmatgiz, M., 1958

[8] Bielawski R., Górniewicz L., Plaskacz S., “Topological approach to differential inclusions on closed subset of $\mathbb R^n$”, Dynam. Report (N.S.), 1 (1992), 225–250 | MR | Zbl