@UNPUBLISHED{publication1, title = "Notes on the spatial part of a frame", author = "{ARRIETA, Igor} and {PICADO, Jorge} and {PULTR, Ales}", year = "2023-05-06", abstract = "

A locale (frame) L has a largest spatial sublocale generated by the primes (spectrum points), the spatial part SpL. In this paper we discuss some of the properties of the embeddings SpL \&\#8838; L. First we analyze the behaviour of the spatial parts in the assembly: the points of L and of S(L)op (\&\#8773; the congruence frame) are in a natural one-one correspondence while the topologies of SpL and Sp(S(L)op) differ. Then we concentrate on some special types of embeddings of SpL into L, namely in the questions when SpL is complemented, closed, or open. While in the first part L was general, here we need some restrictions (weak separation axioms) to obtain suitable formulas.

", url = "http://www.mat.uc.pt/preprints/eng\_2023.html", note = "" }