![]() Engelking, Dimension Theory, North-Holland Publishing Co., Amsterdam, 1978. de Vries, Elements of Topological Dynamics, Kluwer Academic Publishers Group, Dordrecht, 1993. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York, 1981. Vojtáš, Almost disjoint refinements of families of subsets of ℕ, Proc. ![]() Toruńczyk, On CE-images of the Hilbert cube and the characterization of Q-manifolds, Fund. Smith, Concerning the homeomorphisms of the pseudo-arc X as a subspace of C(X×X), Houston J. Nadler, Induced universal maps and some hyperspaces with fixed point property, Proc. Nadler, Hyperspaces of Sets, Marcel Dekker, 1978. Lewis, Pseudo-arc and connectedness in homeomorphism groups, Proc. Kennedy Phelps, Homogeneity and groups of homeomorphisms, Topology Proc. Kennedy, Compactifying the space of homeomorphisms, Colloq. Kelley, Hyperspaces of a continuum, Trans. Kawamura, Span zero continua and the pseudo-arc, Tsukuba J. Schori, Hyperspaces which characterize simple homotopy type, Gen. ![]() Chapman, Lectures on Hilbert Cube Manifolds, CBMS Regional Conf. Brown, Some applications of an approximation theorem for inverse limits, Proc. Bowers, Dense embeddings of nowhere locally compact separable metric spaces, Topology Appl. Bing, A homogeneous indecomposable plane continuum, Duke Math. It is known that H(P) contains no nondegenerate continua (). We also prove that the remainder of H(P) in $G_P$ contains many Hilbert cubes. The author wishes to thank the referee for pointing out the above reference. This is an easy consequence of a combination of the results of, Corollary 2, and, Theorem 1, but here we give a direct proof. We prove that $G_P$ is homeomorphic to the Hilbert cube. 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. Kennedy considered a compactification of H(X) and studied its properties when X has various types of homogeneity. It is well known that H(X) is a completely metrizable, separable topological group. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. TY - JOUR AU - Kawamura, Kazuhiro TI - On a compactification of the homeomorphism group of the pseudo-arc JO - Colloquium Mathematicae PY - 1991 VL - 62 IS - 2 SP - 325 EP - 330 AB - A continuum means a compact connected metric space. We also prove that the remainder of H(P) in G P contains many Hilbert cubes. We prove that G P is homeomorphic to the Hilbert cube. 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. On a compactification of the homeomorphism group of the pseudo-arcĪ continuum means a compact connected metric space.
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