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 of the homeomorphism group of the pseudo-arc P, which is obtained by the method of Kennedy. We prove that 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 contains many Hilbert cubes. It is known that H(P) contains no nondegenerate continua ([10]).
@article{bwmeta1.element.bwnjournal-article-cmv62i2p325bwm,
author = {Kazuhiro Kawamura},
title = {On a compactification of the homeomorphism group of the pseudo-arc},
journal = {Colloquium Mathematicae},
volume = {62},
year = {1991},
pages = {325-330},
zbl = {0790.54042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv62i2p325bwm}
}
Kawamura, Kazuhiro. On a compactification of the homeomorphism group of the pseudo-arc. Colloquium Mathematicae, Tome 62 (1991) pp. 325-330. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv62i2p325bwm/
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