An uncountable collection of mutually incomparable chainable continua

Awartani, Marwan M.

doi:10.1090/S0002-9939-1993-1092914-3

An uncountable collection of mutually incomparable chainable continua
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Proc. Amer. Math. Soc. 118 (1993), 239-245 Request permission

Abstract:

We exhibit the existence of continuum many compactifications of the ray with the arc as remainder, no one of which maps onto any other. We also obtain continuum many pathwise connected circularly chainable continua no one of which maps onto any other. The involved constructions and proofs are combinatorial in nature.

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Pseudo-circles and universal circularly chainable continua