Displaying similar documents to “On the factorizability of maps of S n into S n ”

Spaces with fibered approximation property in dimension n

Taras Banakh, Vesko Valov (2010)

Open Mathematics

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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].

Finite-to-one maps and dimension

Jerzy Krzempek (2004)

Fundamenta Mathematicae

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It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The...

On Surjective Bing Maps

Hisao Kato, Eiichi Matsuhashi (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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In [7], M. Levin proved that the set of all Bing maps of a compact metric space to the unit interval is a dense G δ -subset of the space of all maps. In [6], J. Krasinkiewicz independently proved that the set of all Bing maps of a compact metric space to an n-dimensional manifold (n ≥ 1) is a dense G δ -subset of the space of maps. In [9], J. Song and E. D. Tymchatyn, solving some problems of J. Krasinkiewicz ([6]), proved that the set of all Bing maps of a compact metric space to a nondegenerate...

Kneading sequences for double standard maps

Michael Benedicks, Ana Rodrigues (2009)

Fundamenta Mathematicae

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We investigate the symbolic dynamics for the double standard maps of the circle onto itself, given by f a , b ( x ) = 2 x + a + ( b / π ) s i n ( 2 π x ) ( m o d 1 ) , where b = 1 and a is a real parameter, 0 ≤ a < 1.

Reidemeister conjugacy for finitely generated free fundamental groups

Evelyn L. Hart (2008)

Fundamenta Mathematicae

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Let X be a space with the homotopy type of a bouquet of k circles, and let f: X → X be a map. In certain cases, algebraic techniques can be used to calculate N(f), the Nielsen number of f, which is a homotopy invariant lower bound on the number of fixed points for maps homotopic to f. Given two fixed points of f, x and y, and their corresponding group elements, W x and W y , the fixed points are Nielsen equivalent if and only if there is a solution z ∈ π₁(X) to the equation z = W y - 1 f ♯ ( z ) W x . The Nielsen...