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2010 | 8 | 3 | 411-420
Tytuł artykułu

Spaces with fibered approximation property in dimension n

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EN
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EN
A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: $$ \mathbb{I} $$ m × $$ \mathbb{I} $$ n → M there exists a map g′: $$ \mathbb{I} $$ m × $$ \mathbb{I} $$ n → M such that g′ is ɛ-homotopic to g and dim g′ ({z} × $$ \mathbb{I} $$ n) ≤ n for all z ∈ $$ \mathbb{I} $$ m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
3
Strony
411-420
Opis fizyczny
Daty
wydano
2010-06-01
online
2010-05-30
Twórcy
Bibliografia
  • [1] Banakh T., Valov V., General position properties in fiberwise geometric topology, preprint available at http://arxiv.org/abs/1001.2494
  • [2] Banakh T., Valov V., Approximation by light maps and parametric Lelek maps, preprint available at http://arxiv.org/abs/0801.3107
  • [3] Cauty R., Convexité topologique et prolongement des fonctions continues, Compos. Math., 1973, 27, 233–273 (in French)
  • [4] Matsuhashi E., Valov V., Krasinkiewicz spaces and parametric Krasinkiewicz maps, available at http://arxiv.org/abs/0802.4436
  • [5] Levin M., Bing maps and finite-dimensional maps, Fund. Math., 1996, 151, 47–52
  • [6] Pasynkov B., On geometry of continuous maps of countable functional weight, Fundam. Prikl. Matematika, 1998, 4, 155–164 (in Russian)
  • [7] Repovš D., Semenov P., Continuous selections of multivalued mappings, Mathematics and its Applications, 455, Kluwer Academic Publishers, Dordrecht, 1998
  • [8] Sipachëva O., On a class of free locally convex spaces, Mat. Sb., 2003, 194, 25–52 (in Russian); English translation: Sb. Math., 2003, 194, 333–360
  • [9] Tuncali M., Valov V., On dimensionally restricted maps, Fund. Math., 2002, 175, 35–52 http://dx.doi.org/10.4064/fm175-1-2
  • [10] Tuncali M., Valov V., On finite-dimensional maps II, Topology Appl., 2003, 132, 81–87 http://dx.doi.org/10.1016/S0166-8641(02)00365-6
  • [11] Uspenskij V., A remark on a question of R. Pol concerning light maps, Topology Appl., 2000, 103, 291–293 http://dx.doi.org/10.1016/S0166-8641(99)00030-9
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0027-2
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