On closed and quotient maps of locales

dc.contributor.advisor	Siweya, H.J.
dc.contributor.author	Thoka, Mahuleng Ludwick
dc.date.accessioned	2009-12-14T08:41:53Z
dc.date.available	2009-12-14T08:41:53Z
dc.date.issued	2007
dc.identifier.uri	http://hdl.handle.net/10386/77
dc.description	Thesis (M.Sc. (Mathematics)) --University of Limpopo, 2007	en
dc.description.abstract	The category Loc of locales and continuous maps is dual to the category Frm of frames and frame homomorphisms. Regular subobjects of a locale A are elements of the form Aj = fj : A ! A j j(a) = ag: The subobjects of this form are called sublocales of A. They arise from the lattice OX of open sets of a topological space X in a natural way. The right adjoint of a frame homomorphism maps closed (dually, open) sublocales to closed (dually, open) sublocales. Simple coverings and separated frames are studied and conditions under which they are closed (or open) are those that are related to coequalizers are shown. Under suitable conditions, simple coverings are regular epimorphisms. Extremal epimorphisms and strong epimorphisms in the setting of locales are studied and it is shown that strong epimorphisms compose. In the category Loc of locales and continuous maps, closed surjections are regular epimorphisms at least for those surjections with subfit domains.	en
dc.description.sponsorship	National Research Foundation	en
dc.language.iso	en	en
dc.subject	Maps (Mathematics)	en
dc.subject.lcsh	Mappings (Mathematics)	en
dc.title	On closed and quotient maps of locales	en
dc.type	Thesis	en