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Proceedings of the American Mathematical Society

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

 

 

$ d$-final continua


Author: John Isbell
Journal: Proc. Amer. Math. Soc. 104 (1988), 953-964
MSC: Primary 54F25; Secondary 54D35, 54F05, 54F50
DOI: https://doi.org/10.1090/S0002-9939-1988-0964879-1
MathSciNet review: 964879
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0964879-1
Keywords: Peano continuum, tree, irreducible map, locale
Article copyright: © Copyright 1988 American Mathematical Society