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

• Autorzy: Kazuhiro Kawamura
• Języki publikacji: EN

Abstrakty

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]).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1991
• Tom: 62
• Numer: 2
• Strony: 325-330

Daty

wydano

1991

otrzymano

1989-10-24

poprawiono

1990-08-30

Twórcy

autor

Kazuhiro Kawamura

• Institute of Mathematics, University of Tsukuba, Tsukuba-city, Ibaraki 305, Japan

Bibliografia

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