Souslin dendrons

van Mill, J.; Wattel, E.

doi:10.1090/S0002-9939-1978-0509253-0

Souslin dendrons
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by J. van Mill and E. Wattel

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

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

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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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