Strongly sequential spaces

Frédéric Mynard

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 143-153
  • ISSN: 0010-2628

Abstract

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The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces.

How to cite

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Mynard, Frédéric. "Strongly sequential spaces." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 143-153. <http://eudml.org/doc/22471>.

@article{Mynard2000,
abstract = {The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces.},
author = {Mynard, Frédéric},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sequential; Fréchet; strongly Fréchet topology; product convergence; Antoine convergence; continuous convergence; sequential; strongly sequential; Fréchet; Tanaka topology},
language = {eng},
number = {1},
pages = {143-153},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Strongly sequential spaces},
url = {http://eudml.org/doc/22471},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Mynard, Frédéric
TI - Strongly sequential spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 143
EP - 153
AB - The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces.
LA - eng
KW - sequential; Fréchet; strongly Fréchet topology; product convergence; Antoine convergence; continuous convergence; sequential; strongly sequential; Fréchet; Tanaka topology
UR - http://eudml.org/doc/22471
ER -

References

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  4. Dolecki S., Mynard F., Convergence theoretic mechanisms behind product theorems, to appear in Topology Appl. Zbl0953.54002MR1780899
  5. Engelking R., Topology, PWN, 1977. Zbl0932.01059
  6. Michael E., A quintuple quotient quest, Gen. Topology Appl. 2 91-138 (1972). (1972) Zbl0238.54009MR0309045
  7. Michael E., Local compactness and cartesian product of quotient maps and k -spaces, Ann. Inst. Fourier (Grenoble) 19 281-286 (1968). (1968) MR0244943
  8. Mynard F., Coreflectively modified continuous duality applied to classical product theorems, to appear. Zbl1007.54008MR1890032
  9. Olson R.C., Biquotient maps, countably bisequential spaces and related topics, Topology Appl. 4 1-28 (1974). (1974) MR0365463
  10. Tanaka Y., Products of sequential spaces, Proc. Amer. Math. Soc. 54 371-375 (1976). (1976) Zbl0292.54025MR0397665
  11. Tanaka Y., Necessary and sufficient conditions for products of k -spaces, Topology Proc. 14 281-312 (1989). (1989) Zbl0727.54012MR1107729

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