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Slender modules, endo-slender abelian groups and large cardinals

Katsuya Eda — 1990

Fundamenta Mathematicae

The Dugundji extension theorem and extension degree

Katsuya Eda — 1995

Colloquium Mathematicae

Homotopy types of one-dimensional Peano continua

Katsuya Eda — 2010

Fundamenta Mathematicae

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.

Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda; Kazuhiro Kawamura — 2000

Fundamenta Mathematicae

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 $H_{n} (X \lor Y) ≃ H_{n} (X) \oplus H_{n} (Y) \oplus H_{n} (C X \lor C Y)$ for n ≥ 1.

Covering maps over solenoids which are not covering homomorphisms

Katsuya Eda; Vlasta Matijević — 2013

Fundamenta Mathematicae

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...

A construction of noncontractible simply connected cell-like two-dimensional Peano continua

Katsuya Eda; Umed H. Karimov; Dušan Repovš — 2007

Fundamenta Mathematicae

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,...

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Currently displaying 1 – 6 of 6

Slender modules, endo-slender abelian groups and large cardinals

The Dugundji extension theorem and extension degree

Homotopy types of one-dimensional Peano continua

Homotopy and homology groups of the n-dimensional Hawaiian earring

Covering maps over solenoids which are not covering homomorphisms

A construction of noncontractible simply connected cell-like two-dimensional Peano continua