𝑑-final continua

Isbell, John

doi:10.1090/S0002-9939-1988-0964879-1

$d$-final continua
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by John Isbell

Proc. Amer. Math. Soc. 104 (1988), 953-964

DOI: https://doi.org/10.1090/S0002-9939-1988-0964879-1

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Abstract:

The Hilbert cube is known to be an irreducible quotient of every perfect metric space. Its irreducible quotients are identified: all nondegenerate Peano continua no open set in which is homeomorphic with $R$. In compact metric spaces, every irreducible surjection $X \to Y$ embeds a dense ${G_\delta }$ subset of $X$ in $Y$. The Peano continua I which are strongly initial, every irreducible map from a Peano continuum to I being a homeomorphism, are identified: the dendrites the closure of whose end points is zero-dimensional.

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