Souslin dendrons

Authors:
J. van Mill and E. Wattel

Journal:
Proc. Amer. Math. Soc. **72** (1978), 545-555

MSC:
Primary 54F50

DOI:
https://doi.org/10.1090/S0002-9939-1978-0509253-0

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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Additional Information

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