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 
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/
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     title = {Double convergence and products of {Fr\'echet} spaces},
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     mrnumber = {1624303},
     zbl = {0954.46002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1998_48_2_a1/}
}
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