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1
Content available remote

The Dugundji extension theorem and extension degree

100%
Eda K.
Colloquium Mathematicum
|
1995
|
tom 68
|
nr 1
25-38
2
Content available remote

Homotopy types of one-dimensional Peano continua

100%
Eda K.
Fundamenta Mathematicae
|
2010
|
tom 209
|
nr 1
27-42
EN
Let X and Y be one-dimensional Peano continua. If the fundamental groups of X and Y are isomorphic, then X and Y are homotopy equivalent. Every homomorphism from the fundamental group of X to that of Y is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.
3
Content available remote

Covering maps over solenoids which are not covering homomorphisms

64%
Eda K., Matijević V.
Fundamenta Mathematicae
|
2013
|
tom 221
|
nr 1
69-82
EN
Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and Fox's notion of an overlay map, we answer the question in the negative. We consider infinite-sheeted covering maps over solenoids, i.e. compact connected 1-dimensional abelian groups. First we show that an infinite-sheeted covering map f: X → Σ with a total space being connected over a solenoid Σ does not admit a topological group structure on X such that f becomes a homomorphism. Then, for an arbitrary solenoid Σ, we construct a connected space X and an infinite-sheeted covering map f: X → Σ, which provides a negative answer to the question.
4
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Homotopy and homology groups of the n-dimensional Hawaiian earring

64%
Eda K., Kawamura K.
Fundamenta Mathematicae
|
2000
|
tom 165
|
nr 1
17-28
EN
For the n-dimensional Hawaiian earring $ℍ_n,$ n ≥ 2, $π _n(ℍ_n,o)≃ ℤ^ω$ and $π_i(ℍ_n, o)$ is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then $H_n(X∨Y) ≃ H_{n}(X) ⊕ H_n(Y) ⊕ H_{n}(CX∨CY)$ for n ≥ 1.
5
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A construction of noncontractible simply connected cell-like two-dimensional Peano continua

51%
Eda K., Karimov U., Repovš D.
Fundamenta Mathematicae
|
2007
|
tom 195
|
nr 3
193-203
EN
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.
6
Content available remote

Slender modules, endo-slender abelian groups and large cardinals

38%
Eda K.
Fundamenta Mathematicae
|
1990
|
tom 135
|
nr 1
5-24
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