d-Frames as algebraic duals of bitopological spaces

Jakl, Tomáš (2018). d-Frames as algebraic duals of bitopological spaces. University of Birmingham. Ph.D.

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Achim Jung and Drew Moshier developed a Stone-type duality theory for bitopological spaces, amongst others, as a practical tool for solving a particular problem in the theory of stably compact spaces. By doing so they discovered that the duality of bitopological spaces and their algebraic counterparts, called d-frames, covers several of the known dualities.

In this thesis we aim to take Jung's and Moshier's work as a starting point and fill in some of the missing aspects of the theory. In particular, we investigate basic categorical properties of d-frames, we give a Vietoris construction for d-frames which generalises the corresponding known Vietoris constructions for other categories, and we investigate the connection between bispaces and a paraconsistent logic and then develop a suitable (geometric) logic for d-frames.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Computer Science
Funders: Other
Other Funders: Fond Mobility UK
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
URI: http://etheses.bham.ac.uk/id/eprint/8380


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