id: 05641910
dt: j
an: 05641910
au: Denniston, J.T.; Rodabaugh, S.E.
ti: Functorial relationships between lattice-valued topology and topological
    systems.
so: Quaest. Math. 32, No. 2, 139-186 (2009).
py: 2009
pu: NISC (National Inquiry Services Centre), Grahamstown; Taylor \& Francis,
    Abingdon
la: EN
cc: 
ut: locales; frames; variable-basis topology; stratified spaces; finite
    observational logic; topological category; lattice-valued topology;
    topological systems
ci: 
li: doi:10.2989/QM.2009.32.2.1.794
ab: Authors’ abstract: “This paper investigates functorial relationships
    between lattice-valued topology (arising from fuzzy sets and fuzzy
    logic) and topological systems (arising from topological and localic
    aspects of domains and finite observational logic in computer science).
    Two such relationships are embeddings from TopSys into Loc-Top, both
    having two-fold significance: for computer science the significance is
    that TopSys is not topological over Set $\times $ Loc, yet Loc-Top is
    topological over Set $\times $ Loc; hence these embeddings can be used
    to construct in Loc-Top the unique initial [final] lifts of all
    forgetful functor structured sources [sinks] in TopSys; and for
    topology, the significance is that both embeddings generate
    anti-stratified topological spaces from ordinary topological spaces and
    spatial locales rewritten as topological systems, thus justifying the
    current structural axioms of Loc-Top and lattice-valued topology (which
    include all anti-stratified, non-stratified, and stratified spaces).”
rv: Tomasz Kubiak (Poznań)