Double convergence and products of Fréchet spaces

Josef Novák

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 2, page 207-227
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Novák, Josef. "Double convergence and products of Fréchet spaces." Czechoslovak Mathematical Journal 48.2 (1998): 207-227. <http://eudml.org/doc/30414>.

@article{Novák1998,
abstract = {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.},
author = {Novák, Josef},
journal = {Czechoslovak Mathematical Journal},
keywords = {double sequences; Fréchet space; convergence space},
language = {eng},
number = {2},
pages = {207-227},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Double convergence and products of Fréchet spaces},
url = {http://eudml.org/doc/30414},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Novák, Josef
TI - Double convergence and products of Fréchet spaces
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 207
EP - 227
AB - 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.
LA - eng
KW - double sequences; Fréchet space; convergence space
UR - http://eudml.org/doc/30414
ER -

References

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  9. On some topological spaces represented by systems of sets, Topology and its Applications (Proc. Int. Symposium, Herceg-Novi, 1968). Beograd, 1969, pp. 269–270. (1969) 
  10. 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. MR0448277
  11. 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. (1985) MR0835491
  12. A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolinae 21 (1980), 749–753. (1980) Zbl0466.54022MR0597764

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