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Proceedings of the American Mathematical Society

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

 

 

Separation by finite sets in connected, continuous images of ordered compacta


Author: L. B. Treybig
Journal: Proc. Amer. Math. Soc. 74 (1979), 326-328
MSC: Primary 54F20; Secondary 54C05, 54F05, 54F50
MathSciNet review: 524311
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Abstract: In this paper we answer a question of Mardešić by showing that if the points x and y lie in a continuum M which is the continuous image of a compact ordered space, but x and y lie in no metric subcontinuum of M, then x and y are separated in M by a finite set.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0524311-3
Keywords: Compact ordered space, arc, local connectivity, indecomposable continuum, irreducible continuum, upper semicontinuous decomposition
Article copyright: © Copyright 1979 American Mathematical Society