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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The structure of nested spaces

Authors: T. B. Muenzenberger and R. E. Smithson
Journal: Trans. Amer. Math. Soc. 201 (1975), 57-87
MSC: Primary 54F05
MathSciNet review: 0355995
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Abstract: The structure of nested spaces is studied in this paper using such tools as branches, chains, partial orders, and rays in the context of semitrees. A classification scheme for various kinds of acyclic spaces is delineated in terms of semitrees. Several families of order compatible topologies for semitrees are investigated, and these families are grouped in a spectrum (inclusion chain) of topologies compatible with the semitree structure. The chain, interval, and tree topologies are scrutinized in some detail. Several topological characterizations of semitrees with certain order compatible topologies are also derived.

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Keywords: Acyclic spaces, arboroids, arcs, box topology, branches, chain topology, combs, fans, nested spaces, order compatible topologies, partially ordered spaces, semitrees, trees
Article copyright: © Copyright 1975 American Mathematical Society

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