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)

 
 

 

Regular closed maps


Author: R. F. Dickman
Journal: Proc. Amer. Math. Soc. 39 (1973), 414-416
MSC: Primary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1973-0315654-1
MathSciNet review: 0315654
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A subset $ A$ of $ X$ is far from the remainder if whenever $ \mathcal{U}$ is a free open ultrafilter in $ X$ there exists $ U \in \mathcal{U}$ such that $ A \cap {\text{c}}{{\text{l}}_X}U = \emptyset $. A map is regular closed provided that the image of every regular closed set is closed. In this note we use some recent results of G. Viglino to show that every map can be extended to a regular closed map with far from the remainder point inverses. We also relate these maps to several other interesting classes of maps.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C10

Retrieve articles in all journals with MSC: 54C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0315654-1
Keywords: Regular closed maps, absolutely closed maps
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society