Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A20, 52A10

Retrieve articles in all journals with MSC: 52A20, 52A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0470858-6
PII: S 0002-9939(1977)0470858-6
Keywords: Convex sets, Tietze's theorem, strictly monotone sets, stripwise convex sets
Article copyright: © Copyright 1977 American Mathematical Society