Geodesic
On closure of the pre-images of families of mappings
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 491-501 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 49J15, 49J20, 49J45
Keywords: closure; pre-image; mappings 
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     author = {Zaytsev, Oleg},
     title = {On closure of the pre-images of families of mappings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {491--501},
     year = {1998},
     volume = {39},
     number = {3},
     mrnumber = {1666766},
     zbl = {0969.49004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998_39_3_a5/}
}
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Zaytsev, Oleg. On closure of the pre-images of families of mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 3, pp. 491-501. http://geodesic.mathdoc.fr/item/CMUC_1998_39_3_a5/