Geodesic
On a compactification of the homeomorphism group of the pseudo-arc
Colloquium Mathematicum, Tome 62 (1991) no. 2, pp. 325-330.

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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]).
DOI : 10.4064/cm-62-2-325-330

Kazuhiro Kawamura 1

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Kazuhiro Kawamura. On a compactification of the homeomorphism group of the pseudo-arc. Colloquium Mathematicum, Tome 62 (1991) no. 2, pp. 325-330. doi : 10.4064/cm-62-2-325-330. http://geodesic.mathdoc.fr/articles/10.4064/cm-62-2-325-330/

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