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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of maximal connected spaces and maximal arcwise connected spaces


Authors: Bradd Clark and Victor Schneider
Journal: Proc. Amer. Math. Soc. 104 (1988), 1256-1260
MSC: Primary 54D05
MathSciNet review: 969057
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Abstract: The concept of a maximal connected space was developed by J. P. Thomas and maximal connected expansions of the reals were discovered by Guthrie, Stone, Wage, and Simon. This paper gives necessary and sufficient conditions for a space to be maximal connected. Also necessary and sufficient conditions for the join of two connected topologies to be connected are given in the special case that one of the topologies is atomic. Finally the concept of a maximal arcwise connected topology is given and used to show that every connected simplicial complex admits both a maximal arcwise connected extension and a maximal connected extension.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0969057-8
PII: S 0002-9939(1988)0969057-8
Article copyright: © Copyright 1988 American Mathematical Society