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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Souslin dendrons


Authors: J. van Mill and E. Wattel
Journal: Proc. Amer. Math. Soc. 72 (1978), 545-555
MSC: Primary 54F50
MathSciNet review: 509253
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Abstract: A dendron is a continuum in which every two distinct points have a separation point. We call a dendron X a Souslin dendron provided that X satisfies the countable chain condition, is not separable and has the additional property that every countable subset of X is contained in a metrizable subcontinuum of X. We prove that the existence of a Souslin line is equivalent to the existence of a Souslin dendron. In addition, each Souslin dendron is a continuous image of some Souslin continuum.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509253-0
Keywords: Souslin line, dendron, inverse limit, monotone mapping
Article copyright: © Copyright 1978 American Mathematical Society