A characterization of continua that contain no -ods and no -sets

Author:
Eldon J. Vought

Journal:
Proc. Amer. Math. Soc. **109** (1990), 545-551

MSC:
Primary 54F20; Secondary 54F25

DOI:
https://doi.org/10.1090/S0002-9939-1990-1012940-7

MathSciNet review:
1012940

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Abstract: A proper, nondegenerate subcontinuum of a continuum is said to be a -set if, for every continuum and map of onto , some subcontinuum of is mapped by onto . Jim Davis asked whether a simple closed curve is the only atriodic continuum that contains no -set. An affirmative answer is given to this question. The result follows as a corollary to the more general theorem that a continuum contains no -od and has no -set if and only if it is a graph in which every point is contained in a simple closed curve. Properties of this class of graphs are also described.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1012940-7

Keywords:
Continuum,
-set,
-od,
atriodic,
class ,
-continuum,
graph,
monotone upper-semicontinuous decomposition,
quotient space

Article copyright:
© Copyright 1990
American Mathematical Society