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Proceedings of the American Mathematical Society

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



Characterizations of strictly monotone sets

Author: Jean Chan Stanek
Journal: Proc. Amer. Math. Soc. 64 (1977), 112-117
MSC: Primary 52A20; Secondary 52A10
MathSciNet review: 0470858
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Abstract: One natural generalization of convex sets is the concept of strictly monotone sets. In this paper, Tietze’s characterization theorem on convex sets is generalized to strictly monotone sets. The main result is that a closed connected set in the Euclidean plane ${E_2}$ is strictly monotone if and only if it is locally strictly monotone. This theorem is shown to hold in ${E_n}$ with additional hypotheses.

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Keywords: Convex sets, Tietze’s theorem, strictly monotone sets, stripwise convex sets
Article copyright: © Copyright 1977 American Mathematical Society