Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Applications of the $ u$-closure operator


Authors: M. Solveig Espelie, James E. Joseph and Myung H. Kwack
Journal: Proc. Amer. Math. Soc. 83 (1981), 167-174
MSC: Primary 54D35
DOI: https://doi.org/10.1090/S0002-9939-1981-0620006-5
MathSciNet review: 620006
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\text{c}}{{\text{l}}_u}(A)$ be the $ u$-closure of a subset $ A$ of a space. We prove that a space is compact if and only if for each upper-semicontinuous multifunction $ \lambda $ on the space, the multifunction $ \mu $ defined on the space by $ \mu (x) = {\text{c}}{{\text{l}}_u}(\lambda (x))$ assumes a maximal value under set inclusion. We also prove that in a Urysohn-closed space any two subsets with disjoint $ u$-closures are separated by disjoint open subsets. The quotient space induced by identifying those points with identical $ u$-closures is investigated and shown to be $ {T_0}$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D35

Retrieve articles in all journals with MSC: 54D35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0620006-5
Keywords: Compactness, multifunctions, $ u$-closure
Article copyright: © Copyright 1981 American Mathematical Society