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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Refinable maps and $ \theta\sb n$-continua


Authors: E. E. Grace and Eldon J. Vought
Journal: Proc. Amer. Math. Soc. 106 (1989), 231-239
MSC: Primary 54C10; Secondary 54B15, 54C20, 54E45, 54G20
MathSciNet review: 964455
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Abstract: Many properties of continua, e.g., irreducibility, span zero, and various kinds of aposyndesis and unicoherence, are preserved by refinable maps or their inverses. The purpose of this paper is to consider the extent to which the property of being a $ {\theta '_n}$-continuum is preserved by refinable maps or by inverses of refinable maps. One consequence of this study is to generalize results of the first author where the domain or range is a graph. Several of his results are corollaries of ours.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0964455-1
PII: S 0002-9939(1989)0964455-1
Keywords: Refinable map, $ {\theta _n}$-continuum, $ {\theta '_n}$-continuum, tranche, quotient space, induced map, graph, near homeomorphism
Article copyright: © Copyright 1989 American Mathematical Society