Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	Continuity of localic maps
Publication Date:	2020-01-24
Authors:	- Jorge Picado - Ales Pultr
Abstract:	Mending the contravariance of the natural point-free representation of classical spaces and continuous maps one replaces the category of frames by its dual Loc = Frm^op. To make Loc a concrete category one can replace frame homomorphisms by their right Galois adjoints (called then localic maps). This rather formal representation of generalized continuous maps turns out to be surprisingly geometrically satisfactory: we prove that a localic map is characterized among plain maps between underlying sets in terms of preserving closed and open subobjects by preimage. This is, a.o., another justification of defining open localic maps as those with open images (images being understood as the standard set images of plain maps) of open subobjects. We add a few remarks on the openness and completeness of localic maps.
Institution:	DMUC 20-04
Online version:	http://www.mat.uc.pt...prints/eng_2020.html
Download:	Not available