Geodesic
Finite-to-one fuzzy maps and fuzzy perfect maps
Kybernetika, Tome 34 (1998) no. 2, pp. 163-169 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we define, for fuzzy topology, notions corresponding to finite-to-one and $k$-to-one maps. We study the relationship between these new fuzzy maps and various kinds of fuzzy perfect maps. Also, we show the invariance and the inverse inveriance under the various kinds of fuzzy perfect maps (and the finite-to-one fuzzy maps), of different properties of fuzzy topological spaces.
In this paper we define, for fuzzy topology, notions corresponding to finite-to-one and $k$-to-one maps. We study the relationship between these new fuzzy maps and various kinds of fuzzy perfect maps. Also, we show the invariance and the inverse inveriance under the various kinds of fuzzy perfect maps (and the finite-to-one fuzzy maps), of different properties of fuzzy topological spaces.
Classification : 03E72, 04A72, 54A40
Keywords: fuzzy topology; fuzzy perfect maps 
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Lupiáñez, Francisco Gallego. Finite-to-one fuzzy maps and fuzzy perfect maps. Kybernetika, Tome 34 (1998) no. 2, pp. 163-169. http://geodesic.mathdoc.fr/item/KYB_1998_34_2_a2/

[1] Arhangel’skii A. V.: A criterion for the existence of a bicompact element in a continuous decomposition. A theorem on the invariance of weight under open–closed finite–to–one mappings. Soviet Math. Dokl. 7 (1966), 249–253

[2] Arhangel’skii A. V.: A theorem of the metrizability of the inverse image of a metric space under an open–closed finite–to–one mapping. Example and unsolved problems. Soviet Math. Dokl. 7 (1966), 1258–1262 | MR

[3] Chaber J.: Open finite–to–one images of metric spaces. Topology Appl. 14 (1982), 241–246 | DOI | MR | Zbl

[4] Chang C. L.: Fuzzy topological spaces. J. Math. Anal. Appl. 24 (1968), 182–190 | DOI | MR | Zbl

[5] Christoph F. T.: Quotient fuzzy topology and local compactness, J. Math. Anal. Appl. 57 (1977), 497–504 | DOI | MR

[6] Čoban M. M.: Open finite–to–one mappings. Soviet Math. Dokl. 8 (1967), 603–605

[7] El–Monsef M. E. A., Zeyada F. M., El–Deeb S. N., Hanafy I. M.: Good extensions of paracompactness. Math. Japon. 37 (1992), 195–200 | MR | Zbl

[8] Ghosh B.: Directed family of fuzzy sets and fuzzy perfect maps. Fuzzy Sets and Systems 75 (1995), 93–101 | DOI | MR | Zbl

[9] Gittings R. F.: Finite–to–one open maps of generalized metric spaces. Pacific J. Math. 59 (1975), 33–41 | DOI | MR | Zbl

[10] Gittings R. F.: Open mapping theory. In: Set–theoretic Topology (G. M. Reed, ed.), Academic Press, New York 1977, pp. 141–191 | MR | Zbl

[11] Kohli J. K.: Finite–to–one maps and open extensions of maps. Proc. Amer. Math. Soc. 48 (1975), 464–468 | DOI | MR | Zbl

[12] Lowen R.: Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56 (1976), 621–633 | DOI | MR | Zbl

[13] Lowen R.: A comparison of different compactness notions in fuzzy topological spaces. J. Math. Anal. Appl. 64 (1978), 446–454 | DOI | MR | Zbl

[14] Luo M. K.: Paracompactness in fuzzy topological spaces. J. Math. Anal. Appl. 130 (1988), 55–77 | DOI | MR | Zbl

[15] Lupiáñez F. G.: Fuzzy perfect maps and fuzzy paracompactness. Fuzzy Sets and Systems, to appear | MR | Zbl

[16] Martin H. W.: Weakly induced fuzzy topological spaces. J. Math. Anal. Appl. 78 (1980), 634–639 | DOI | MR | Zbl

[17] Okuyama A.: Note on inverse images under finite–to–one mappings. Proc. Japan Acad. 43 (1967), 953–956 | MR

[18] Pareek C. M.: Open finite–to–one mappings on $p$–spaces. Math. Japon. 28 (1983), 9–13 | MR | Zbl

[19] Proizvolov V. V.: Finitely multiple open mappings. Soviet Math. Dokl. 7 (1966), 35–38 | MR

[20] Pu P.–M., Liu Y.–M.: Fuzzy topology I. Neighborhood structure of a fuzzy point and Moore–Smith convergence. J. Math. Anal. Appl. 76 (1980), 571–599 | DOI | MR | Zbl

[21] Sadyrkhanov R. S.: A finite–to–one criterion for covering maps. Soviet Math. Dokl. 28 (1983), 587–590 | Zbl

[22] Shostak A. P.: Two decades of fuzzy topology: basic ideas, notions, and results. Russian Math. Surveys 44 (6) (1989), 125–186 | DOI | MR | Zbl

[23] Srivastava R., Lal S. N.: On fuzzy proper maps. Mat. Vesnik 38 (1986), 337–342 | MR | Zbl

[24] Srivastava R., Lal S. N., Srivastava A. K.: Fuzzy Hausdorff topological spaces, J. Math. Anal. Appl. 81 (1981), 497–506 | DOI | MR

[25] Srivastava R., Lal S. N., Srivastava A. K.: Fuzzy $T_1$–topological spaces. J. Math. Anal. Appl. 102 (1984), 442–448 | DOI | MR

[26] Tanaka Y.: On open finite–to–one maps. Bull. Tokyo Gakugei Univ., Ser. IV, 25 (1973), 1–13. | MR | Zbl

[27] Wong C. K.: Fuzzy topology: product and quotient theorems. J. Math. Anal. Appl. 45 (1974), 512–521 | DOI | MR | Zbl