Stellenbosch University
Maximal nowhere dense sublocales
Mbekezeli Nxumalo, University of South
Africa
SAMS Subject Classification Number: 13
Call a closed nowhere dense sublocale of a completely regular locale \(L\) maximal nowhere dense if it is not nowhere dense in any closed nowhere dense sublocale of \(L\). This concept is a frame counterpart of maximal nowhere dense subsets which were introduced by Veksler (in [1]) in the category of topological spaces. In this talk, I aim to introduce and study maximal nowhere dense sublocales. I will:
show that the concept of maximal nowhere dense subsets is conservative in locales;
show that the definition of inacessible points is conservative in locales and define inaccessible sublocales; and
present results about maximal nowhere dense sublocales using inaccessible sublocales and remote sublocales.
References
[1] A. I. Veksler, Maximal nowhere dense sets in topological spaces, Izv. Vyssh. Uchebn. Zaved. 5 (1975), 9–16.
