Spaces with fibered approximation property in dimension n

• Autorzy: Taras Banakh , Vesko Valov
• Języki publikacji: EN

Abstrakty

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].

Słowa kluczowe

EN

Dimension; n-dimensional maps; Fibered approximation property; Simplicial complex

Kategorie tematyczne

• 55M10: Dimension theory
• 54F45: Dimension theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 3
• Strony: 411-420

Daty

wydano

2010-06-01

online

2010-05-30

Twórcy

autor

Taras Banakh

autor

Vesko Valov

• Nipissing University

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

Identyfikatory

DOI

10.2478/s11533-010-0027-2