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Title: d-Frames as algebraic duals of bitopological spaces
Author: Jakl, Tomáš
ISNI:       0000 0004 7426 2193
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2018
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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.
Supervisor: Not available Sponsor: Fond Mobility
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics ; QA75 Electronic computers. Computer science ; QA76 Computer software