On closure of the pre-images of families of mappings

Oleg Zaytsev

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 3, page 491-501
  • ISSN: 0010-2628

Abstract

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The closures of the pre-images associated with families of mappings in different topologies of normed spaces are considered. The question of finding a description of these closures by means of families of the same kind as original ones is studied. It is shown that for the case of the weak topology this question may be reduced to finding an appropriate closure of a given family. There are discussed various situations when the description may be obtained for the case of the strong topology. An example of a family is constructed which shows that it is, in general, impossible to find such a description for this case.

How to cite

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Zaytsev, Oleg. "On closure of the pre-images of families of mappings." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 491-501. <http://eudml.org/doc/248231>.

@article{Zaytsev1998,
abstract = {The closures of the pre-images associated with families of mappings in different topologies of normed spaces are considered. The question of finding a description of these closures by means of families of the same kind as original ones is studied. It is shown that for the case of the weak topology this question may be reduced to finding an appropriate closure of a given family. There are discussed various situations when the description may be obtained for the case of the strong topology. An example of a family is constructed which shows that it is, in general, impossible to find such a description for this case.},
author = {Zaytsev, Oleg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {closure; pre-image; mappings; closure; pre-image; mappings; -convergence; elliptic two-point boundary-value problem; optimization},
language = {eng},
number = {3},
pages = {491-501},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On closure of the pre-images of families of mappings},
url = {http://eudml.org/doc/248231},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Zaytsev, Oleg
TI - On closure of the pre-images of families of mappings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 3
SP - 491
EP - 501
AB - The closures of the pre-images associated with families of mappings in different topologies of normed spaces are considered. The question of finding a description of these closures by means of families of the same kind as original ones is studied. It is shown that for the case of the weak topology this question may be reduced to finding an appropriate closure of a given family. There are discussed various situations when the description may be obtained for the case of the strong topology. An example of a family is constructed which shows that it is, in general, impossible to find such a description for this case.
LA - eng
KW - closure; pre-image; mappings; closure; pre-image; mappings; -convergence; elliptic two-point boundary-value problem; optimization
UR - http://eudml.org/doc/248231
ER -

References

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