Thesis (M.Sc. (Mathematics)) --University of Limpopo, 2007 / 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. / National Research Foundation
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ul/oai:ulspace.ul.ac.za:10386/77 |
| Date | January 2007 |
| Creators | Thoka, Mahuleng Ludwick |
| Contributors | Siweya, H.J. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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