Klinke, Olaf Karl (2012). A bitopological point-free approach to compactifications. University of Birmingham. Ph.D.
|
Klinke_12_PhD.pdf
Download (1MB) |
Abstract
This thesis extends the concept of compactifications of topological spaces to a setting where spaces carry a partial order and maps are order-preserving. The main tool is a Stone-type duality between the category of d-frames, which was developed by Jung and Moshier, and bitopological spaces. We demonstrate that the same concept that underlies d-frames can be used to do recover short proofs of well-known facts in domain theory. In particular we treat the upper, lower and double powerdomain constructions in this way. The classification of order-preserving compactifications follows ideas of B. Banaschewski and M. Smyth. Unlike in the categories of spaces or locales, the lattice-theoretic notion of normality plays a central role in this work. It is shown that every compactification factors as a normalisation followed by the maximal compactification, the Stone-Cech compactification. Sample applications are the Fell compactification and a stably compact extension of algebraic domains.
Type of Work: | Thesis (Doctorates > Ph.D.) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Award Type: | Doctorates > Ph.D. | ||||||||||||
Supervisor(s): |
|
||||||||||||
Licence: | |||||||||||||
College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | ||||||||||||
School or Department: | School of Computer Science | ||||||||||||
Funders: | Other | ||||||||||||
Other Funders: | The University of Birmingham | ||||||||||||
Subjects: | G Geography. Anthropology. Recreation > GA Mathematical geography. Cartography Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software |
||||||||||||
URI: | http://etheses.bham.ac.uk/id/eprint/3470 |
Actions
Request a Correction | |
View Item |
Downloads
Downloads per month over past year