Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Topological spaces and lattices of lower semicontinuous functions


Author: M. C. Thornton
Journal: Trans. Amer. Math. Soc. 181 (1973), 495-506
MSC: Primary 54C30
MathSciNet review: 0320994
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Lower semicontinuous real-valued functions on a space $ X$ form a conditionally complete distributive lattice $ L(X)$. Those lattices which can be represented as $ L(X)$ for some $ X$ are characterized algebraically. All spaces producing isomorphic lattices ate determined. The class of spaces which are determined by their function lattices is introduced.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54C30

Retrieve articles in all journals with MSC: 54C30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0320994-0
PII: S 0002-9947(1973)0320994-0
Keywords: Lower semicontinuous functions, lattice of closed subsets, fc spaces
Article copyright: © Copyright 1973 American Mathematical Society