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

 

Tietze-type theorems on monotone increasing sets


Author: Jean Chan Stanek
Journal: Proc. Amer. Math. Soc. 54 (1976), 286-290
MathSciNet review: 0388244
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Abstract: The Tietze theorem on convex sets is generalized to monotone increasing sets and strictly monotone increasing sets, which include convex sets as a special case. The main theorem is that a closed connected set in $ {E_2}$ is monotone increasing if and only if it is locally monotone increasing. A similar result is proved for strictly monotone increasing sets.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0388244-5
PII: S 0002-9939(1976)0388244-5
Keywords: Convex sets, Tietze's theorem, local convexity, monotone increasing sets, strictly monotone increasing sets
Article copyright: © Copyright 1976 American Mathematical Society