Geodesic
Double convergence and products of Fréchet spaces
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 2, pp. 207-227
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The paper is devoted to convergence of double sequences and its application to products. In a convergence space we recognize three types of double convergences and points, respectively. We give examples and describe their structure and properties. We investigate the relationship between the topological and convergence closure product of two Fréchet spaces. In particular, we give a necessary and sufficient condition for the topological product of two compact Hausdorff Fréchet spaces to be a Fréchet space.
The paper is devoted to convergence of double sequences and its application to products. In a convergence space we recognize three types of double convergences and points, respectively. We give examples and describe their structure and properties. We investigate the relationship between the topological and convergence closure product of two Fréchet spaces. In particular, we give a necessary and sufficient condition for the topological product of two compact Hausdorff Fréchet spaces to be a Fréchet space.
Classification : 46A04, 46A19, 54A20 
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}
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Novák, Josef. Double convergence and products of Fréchet spaces. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 2, pp. 207-227. http://geodesic.mathdoc.fr/item/CMJ_1998_48_2_a1/

[AR79] Arhangel’skiǐ, A. V.: The frequency spectrum of a topological space and the product operation. Trudy Moskovs. Mat. Obshch. 40 (1979), 171–206. (Russian) | MR

[BR74] Boehme, T. K. and Rosenfeld, M.: An example of two compact Fréchet Hausdorff spaces, whose product is not Fréchet. J. London Math. Soc. 8 (1974), 339–344. | DOI | MR

[FV85] Frič, R. and Vojtáš, P.: Diagonal conditions in sequential convergence. Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyně, 1984), Akademie-Verlag, Mathematical Research/ Mathematische Forschung Bd. 24, Berlin, 1985, pp. 77–94. | MR

[KC75] Kendrick, C. T.: On products of Fréchet spaces. Math. Nachr. 65 (1975), 117–123. | DOI | MR | Zbl

[KE71] Kent, D. C.: Decisive convergence spaces, sequential spaces, and Fréchet spaces. Rocky Mtn. J. Math. 1 (1971), 367–374. | DOI | MR

[KO85] Koutník, V.: Closure and topological sequential convergence. Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyně, 1984), Akademie-Verlag, Mathematical Research/Mathematische Forschung Bd. 24, Berlin, 1985, pp. 199–204. | MR

[KR77] Kratochvíl, P.: Multisequences and measure. Gnereal Topology and its Relations to Modern Analysis and Algebra, IV (Proc. Fourth Prague Topological Sympos., 1976) Part B Contributed Papers, Society of Czechoslovak Mathematicians and Physicists, Praha 1977, pp. 237–244. | MR

[MI72] Michael, E.: A quintuple quotient quest. Gen. Top. Appl. 2. (1972), 91–138. | MR

[NO69] Novák, J.: On some topological spaces represented by systems of sets. Topology and its Applications (Proc. Int. Symposium, Herceg-Novi, 1968). Beograd, 1969, pp. 269–270.

[NO77] Novák, J.: Concerning the topological product of two Fréchet spaces. Gnereal Topology and its Relations to Modern Analysis and Algebra, IV (Proc. Fourth Prague Topological Sympos., 1976), Part B Contributed Papers, Society of Czechoslovak Mathematicians and Physicists, Praha 1977, pp. 342–343. | MR

[NO85] Novák, J.: Convergence of double sequences. Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyně, 1984), Akademie-Verlag, Mathematical Research/ Mathematische Forschung Bd. 24, Berlin, 1985, pp. 233–243. | MR

[SI80] Simon, P.: A compact Fréchet space whose square is not Fréchet. Comment. Math. Univ. Carolinae 21 (1980), 749–753. | MR | Zbl