COMPATIBILITY OF EXTENSIONS OF A COMBINATORIAL GEOMETRY
| dc.contributor.author | Cheung, Alan | |
| dc.date.accessioned | 2016-09-29T14:44:48Z | |
| dc.date.available | 2016-09-29T14:44:48Z | |
| dc.date.issued | 2016-09-29 | |
| dc.date.submitted | 1974 | |
| dc.description.abstract | Two extensions of a geometry are compatible with each other if they have a common extension. If the given extensions are elementary, their compatibility can be intrinsically described in terms of their corresponding linear subclasses. Certain adjointness relation between an extension of a geometry and the geometry itself is also discussed. Any extension of a geometry G by a geometry F determines and is determined by a unique quotient bundle on G indexed by F. As a study of the compatibility among given quotients of a geometry, we look at the possibility of completing to F-bundles a family of quotients indexed by a set I of flats of F. If the indexing geometry F is free and if the set I is a Boolean subalgebra or a sublattice of F, for any family Q(I) of quotients of a geometry G, there is a canonical construction which determines its completability and at the same time produces the extremal completion if it is a partial bundle. Geometries studied in this dissertation are furnished with the weak order. Almost invariably, the Higgs' lift construction, in a somewhat generalized sense, constitutes a convenient and indispensable means in various of the extremal constructions. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/10966 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | combinatorial geometries | en |
| dc.subject | elementary extensions | en |
| dc.subject | strong maps | en |
| dc.subject | orthogonality | en |
| dc.subject | compatibility theorems | en |
| dc.subject | quotient bundles | en |
| dc.subject | lift and drop sequences | en |
| dc.subject | linear subclass generating sequence | en |
| dc.subject | weak order | en |
| dc.title | COMPATIBILITY OF EXTENSIONS OF A COMBINATORIAL GEOMETRY | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws-etd.degree.discipline | Pure Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws.contributor.advisor | Crapo, Henry H. | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |