Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Spaces with fibered approximation property in dimension n

100%

Banakh T., Valov V.

Open Mathematics

2010

tom 8

nr 3

411-420

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].

On the dimension of the space of ℝ-places of certain rational function fields

64%

Banakh T., Kholyavka Y., Potyatynyk O., Machura M., Kuhlmann K.

Open Mathematics

2014

tom 12

nr 8

1239-1248

We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.

Ograniczanie wyników

2 Open Mathematics

2 Banakh T.

1 Kholyavka Y.

1 Kuhlmann K.

1 Machura M.

1 Potyatynyk O.

1 Valov V.

1 2014

1 2010

Wyniki wyszukiwania

Spaces with fibered approximation property in dimension n

On the dimension of the space of ℝ-places of certain rational function fields