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1
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Low dimensional homotopy groups of suspensions of the Hawaiian earring

100%
Kawamura K.
Colloquium Mathematicum
|
2003
|
tom 96
|
nr 1
27-39
EN
We study the (n+1)st homotopy groups and the shape groups of the (n-1)-fold reduced and unreduced suspensions of the Hawaiian earring.
2
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A note on singular homology groups of infinite products of compacta

100%
Kawamura K.
Fundamenta Mathematicae
|
2002
|
tom 175
|
nr 3
285-289
EN
Let n be an integer with n ≥ 2 and ${X_{i}}$ be an infinite collection of (n-1)-connected continua. We compare the homotopy groups of $Σ(∏_{i}X_{i})$ with those of $∏_{i}ΣX_{i}$ (Σ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the n(≥ 2)-sphere is given.
3
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On a compactification of the homeomorphism group of the pseudo-arc

100%
Kawamura K.
Colloquium Mathematicum
|
1991
|
tom 62
|
nr 2
325-330
EN
A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification $G_P$ of the homeomorphism group of the pseudo-arc P, which is obtained by the method of Kennedy. We prove that $G_P$ is homeomorphic to the Hilbert cube. This is an easy consequence of a combination of the results of [2], Corollary 2, and [9], Theorem 1, but here we give a direct proof. The author wishes to thank the referee for pointing out the above reference [2]. We also prove that the remainder of H(P) in $G_P$ contains many Hilbert cubes. It is known that H(P) contains no nondegenerate continua ([10]).
4
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Approximations of Stone-Cech compactifications by Higson compactifications

64%
Kawamura K., Tomoyasu K.
Colloquium Mathematicum
|
2001
|
tom 88
|
nr 1
75-92
EN
The Higson compactification $X̅^{d}$ of a non-compact proper metric space (X,d) is rarely equivalent to the Stone-Čech compactification βX. We give a characterization of such spaces. Also, we show that for each non-compact locally compact separable metric space, βX is equivalent to $lim\limits_{⟵ }{X̅^{d}: d$ is a proper metric on X which is compatible with the topology of X}. The approximation method of the above type is illustrated by some examples and applications.
5
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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.
6
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On homogeneous totally disconnected 1-dimensional spaces

51%
Kawamura K., Oversteegen L. G., Tymchatyn E. D.
Fundamenta Mathematicae
|
1996
|
tom 150
|
nr 2
97-112
EN
The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular, we will show that the set of endpoints of the universal separable ℝ-tree, the set of endpoints of the Julia set of the exponential map, the set of points in Hilbert space all of whose coordinates are irrational and the set of endpoints of the Lelek fan are all homeomorphic. Moreover, we show that these spaces satisfy a topological scaling property: all non-empty open subsets and all complements of σ-compact subsets are homeomorphic.
7
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Topological type of weakly closed subgroups in Banach spaces

51%
Dobrowolski T., Grabowski J., Kawamura K.
Studia Mathematica
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1996
|
tom 118
|
nr 1
49-62
EN
The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in $ℓ^1$ which are interesting from the Banach space theory point of view are discussed.
8
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Another application of the Effros theorem to the pseudo-arc

45%
Kawamura K., Prajs J. R.
Fundamenta Mathematicae
|
1991
|
tom 137
|
nr 3
147-155
9
Content available remote

Some productive classes of maps which arc related to confluent maps

44%
Kawamura K.
Fundamenta Mathematicae
|
1991
|
tom 138
|
nr 3
175-191
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