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Tietze-type theorems on monotone increasing sets


Author: Jean Chan Stanek
Journal: Proc. Amer. Math. Soc. 54 (1976), 286-290
DOI: https://doi.org/10.1090/S0002-9939-1976-0388244-5
MathSciNet review: 0388244
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Abstract | References | Additional Information

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.


References [Enhancements On Off] (What's this?)

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Additional Information

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

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