Tomáš Jakl

d-Frames as algebraic duals of bitopological spaces

(Ph.D. thesis, 2017/12/28)

Abstract

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.

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BibTex

@phdthesis{jakl2018,
     title = {d-Frames as algebraic duals of bitopological spaces},
    school = {Charles University and University of Birmingham},
    author = {Tom{\'a}{\v s} Jakl},
      year = {2018},
       url = {http://etheses.bham.ac.uk/8380/}
}