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)

 

Functions with a dense set of proper local maximum points


Author: Alfonso Villani
Journal: Proc. Amer. Math. Soc. 94 (1985), 353-359
MSC: Primary 54C30; Secondary 26B05, 54E35
MathSciNet review: 784192
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be any metric space. The existence of continuous real functions on $ X$, with a dense set of proper local maximum points, is shown. Indeed, given any $ \sigma $-discrete set $ S \subset X$, the set of all $ f \in C(X)$, which assume a proper local maximum at each point of $ S$, is a dense subset of $ C(X)$. This implies, for a perfect metric space $ X$, the density in $ C(X,Y)$ of "nowhere constant" continuous functions from $ X$ to a normed space $ Y$. In this way, two questions raised in [2] are solved.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C30, 26B05, 54E35

Retrieve articles in all journals with MSC: 54C30, 26B05, 54E35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0784192-2
PII: S 0002-9939(1985)0784192-2
Article copyright: © Copyright 1985 American Mathematical Society