The fundamental group of one-dimensional spaces
نویسندگان
چکیده
منابع مشابه
Fundamental Groups of One-dimensional Spaces
Let X be a metrizable one-dimensional continuum. In the present paper we describe the fundamental group of X as a subgroup of its Čech homotopy group. In particular, the elements of the Čech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental g...
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We study the fundamental group of one–dimensional spaces. Among the results we prove are that the fundamental group of a second countable, connected, locally path connected, one–dimensional metric space is free if and only if it is countable if and only if the space has a universal cover and that the fundamental group of a compact, one–dimensional, connected metric space embeds in an inverse li...
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We show that the Bruschlinsky group with the winding order is a homeomorphism 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 ...
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In the study of topology, we are often interested in understanding and classifying the internal structure of topological spaces. Algebraic topology is the application of abstract algebra to topology in order to further identify the structure of topological spaces by developing a correspondence between topological spaces and certain groups called homotopy groups. In this paper, we will examine t...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1959
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1959-0105102-1