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Proceedings of the American Mathematical Society

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

 
 

 

$\sigma$-coherent continua are hereditarily locally connected


Authors: M. R. Hagan and W. S. Mahavier
Journal: Proc. Amer. Math. Soc. 81 (1981), 129-132
MSC: Primary 54F20; Secondary 54F55
DOI: https://doi.org/10.1090/S0002-9939-1981-0589154-2
MathSciNet review: 589154
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Abstract: A $\sigma$-coherent continuum is one in which every descending sequence of connected sets has a connected intersection. In this paper it is proved that such continua are hereditarily locally connnected. An example is given to show that the converse is not true.


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Keywords: Hereditarily locally connected, regular continuum, <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-coherent
Article copyright: © Copyright 1981 American Mathematical Society