A bitopological point-free approach to compactifications

Klinke, Olaf Karl (2012). A bitopological point-free approach to compactifications. University of Birmingham. Ph.D.

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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):
Supervisor(s)EmailORCID
Jung , AchimUNSPECIFIEDUNSPECIFIED
Escardo, MartinUNSPECIFIEDUNSPECIFIED
Vickers, StevenUNSPECIFIEDUNSPECIFIED
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

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