Geodesic
lp(R)-equivalence of topological spaces and topological modules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2015), pp. 20-47.

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Let R be a topological ring and E be a unitary topological R-module. Denote by Cp(X,E) the class of all continuous mappings of X into E in the topology of pointwise convergence. The spaces X and Y are called lp(E)-equivalent if the topological R-modules Cp(X,E) and Cp(Y,E) are topological isomorphisms. Some conditions under which the topological property P is preserved by the lp(E)-equivalence (Theorems 8–11) are given. 
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Mitrofan M. Choban; Radu N. Dumbrăveanu. $l_p(R)$-equivalence of topological spaces and topological modules. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2015), pp. 20-47. https://geodesic-test.mathdoc.fr/item/BASM_2015_1_a2/

[1] Arhangel'skii A. V., Topological Function Spaces, Mathematics and its Applications (Soviet Series), 78, Kluwer Academic Publishers Group, Dordrecht, 1992 | MR

[2] Soviet Math. Dokl., 25 (1982), 852–855 | MR

[3] Choban M. M., “General theorems on functional equivalence of topological spaces”, Topology Appl., 89 (1998), 223–239 | MR | Zbl

[4] Choban M. M., “Algebraical equivalence of topological spaces”, Bul. Acad. de Ştiinţe Repub. Moldova, Mat., 2001, no. 1(35), 12–36 | MR | Zbl

[5] Choban M. M., “Finite-to-one open mappings”, Dokl. Acad. Nauk SSSR, 174 (1967), 41–44 | MR | Zbl

[6] Trans. Moscow Math. Soc., 48 (1986), 115–159 | MR | Zbl

[7] Choban M. M., “Some topics in topological algebra”, Topology Appl., 54 (1993), 183–202 | MR | Zbl

[8] van Mill J., The infinite-dimensional topology of function spaces, North-Holland Mathematical Library, 64, Amsterdam, 2001 | MR | Zbl

[9] Okuyama A., “A survey of the theory of $\sigma$-spaces”, General Topology Appl., 1 (1971), 57–63 | MR | Zbl

[10] Valov V., “Function spaces”, Topology Appl., 81:1 (1997), 1–22 | MR | Zbl

[11] Warner S., Topological rings, North-Holland mathematics studies, 178, Elsevier, 1993 | MR