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On a characterization of the unit interval in terms of clones

Artur Barkhudaryan (1999)

Commentationes Mathematicae Universitatis Carolinae

This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.

On composants of solenoids

Ronald de Man (1995)

Fundamenta Mathematicae

It is proved that any two composants of any two solenoids are homeomorphic.

On homogeneous totally disconnected 1-dimensional spaces

Kazuhiro Kawamura, Lex Oversteegen, E. 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,...

Ordered group invariants for one-dimensional spaces

Inhyeop Yi (2001)

Fundamenta Mathematicae

We show that the Bruschlinsky group with the winding order is a homomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.

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