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Double convergence and products of Fréchet spaces. (English) Zbl 0954.46002
The paper is devoted to convergence of double sequences and its application to products. In a convergence space three types of double convergences and points, respectively, are recognized; examples are given and their structure and properties are described. The relationship between the topological and convergence closure product of two Fréchet spaces is investigated. In particular, necessary and sufficient condition is given for the topological product of two compact Hausdorff Fréchet spaces to be a Fréchet space.
Reviewer: A.Kufner (Praha)

##### MSC:
 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $$\mathbb{R}$$, etc.) 46A04 Locally convex Fréchet spaces and (DF)-spaces
##### Keywords:
double sequences; Fréchet space; convergence space
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##### References:
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