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On a compactification of the homeomorphism group of the pseudo-arc

Kazuhiro Kawamura — 1991

Colloquium Mathematicae

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...

A note on singular homology groups of infinite products of compacta

Kazuhiro Kawamura — 2002

Fundamenta Mathematicae

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 Σ X 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.

Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya EdaKazuhiro Kawamura — 2000

Fundamenta Mathematicae

For the n-dimensional Hawaiian earring n , n ≥ 2, π n ( n , o ) ω and π i ( 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 ( C X C Y ) for n ≥ 1.

On homogeneous totally disconnected 1-dimensional spaces

Kazuhiro KawamuraLex OversteegenE. Tymchatyn — 1996

Fundamenta Mathematicae

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,...

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