Publication at Faculty of Mathematics and Physics |
2017
Abstract
Generalizing the obvious representation of a subspace as a sublocale in Omega(X) by the congruence {(U,V)|U \cup Y=V\cup Y}, one obtains another congruence, first with sublocales S of a frame L, which (as it is well known) produces back the sublocale S itself, and then with general subsets. The relation of such S with the sublocale produced is studied (the result is not always the sublocale generated by S).
Further, we discuss in general the associated adjunctions, in particular that between relations on L and subsets of L and view the aforementioned phenomena in this perspective.