Spaces with fibered approximation property in dimension n

Taras Banakh; Vesko Valov

Open Mathematics (2010)

  • Volume: 8, Issue: 3, page 411-420
  • ISSN: 2391-5455

Abstract

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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: 𝕀 m × 𝕀 n → M there exists a map g′: 𝕀 m × 𝕀 n → M such that g′ is ɛ-homotopic to g and dim g′ (z × 𝕀 n) ≤ n for all z ∈ 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].

How to cite

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Taras Banakh, and Vesko Valov. "Spaces with fibered approximation property in dimension n." Open Mathematics 8.3 (2010): 411-420. <http://eudml.org/doc/269284>.

@article{TarasBanakh2010,
abstract = {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].},
author = {Taras Banakh, Vesko Valov},
journal = {Open Mathematics},
keywords = {Dimension; n-dimensional maps; Fibered approximation property; Simplicial complex; dimension; -dimensional maps; fibered approximation property; simplicial complex},
language = {eng},
number = {3},
pages = {411-420},
title = {Spaces with fibered approximation property in dimension n},
url = {http://eudml.org/doc/269284},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Taras Banakh
AU - Vesko Valov
TI - Spaces with fibered approximation property in dimension n
JO - Open Mathematics
PY - 2010
VL - 8
IS - 3
SP - 411
EP - 420
AB - 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].
LA - eng
KW - Dimension; n-dimensional maps; Fibered approximation property; Simplicial complex; dimension; -dimensional maps; fibered approximation property; simplicial complex
UR - http://eudml.org/doc/269284
ER -

References

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  1. [1] Banakh T., Valov V., General position properties in fiberwise geometric topology, preprint available at http://arxiv.org/abs/1001.2494 Zbl1301.57019
  2. [2] Banakh T., Valov V., Approximation by light maps and parametric Lelek maps, preprint available at http://arxiv.org/abs/0801.3107 Zbl1223.54047
  3. [3] Cauty R., Convexité topologique et prolongement des fonctions continues, Compos. Math., 1973, 27, 233–273 (in French) Zbl0275.54015
  4. [4] Matsuhashi E., Valov V., Krasinkiewicz spaces and parametric Krasinkiewicz maps, available at http://arxiv.org/abs/0802.4436 Zbl1221.54041
  5. [5] Levin M., Bing maps and finite-dimensional maps, Fund. Math., 1996, 151, 47–52 Zbl0860.54028
  6. [6] Pasynkov B., On geometry of continuous maps of countable functional weight, Fundam. Prikl. Matematika, 1998, 4, 155–164 (in Russian) Zbl0963.54025
  7. [7] Repovš D., Semenov P., Continuous selections of multivalued mappings, Mathematics and its Applications, 455, Kluwer Academic Publishers, Dordrecht, 1998 Zbl0915.54001
  8. [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 Zbl1079.54014
  9. [9] Tuncali M., Valov V., On dimensionally restricted maps, Fund. Math., 2002, 175, 35–52 http://dx.doi.org/10.4064/fm175-1-2 Zbl1021.54027
  10. [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 Zbl1029.54042
  11. [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 

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