Completion of Lattices of Semi-continuous Functions
نویسندگان
چکیده
If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued functions on certain bitopological spaces. The distributivity of certain lattices is investigated, and the theorem of Funayama on distributive normal completions is generalized. Subject classification {Atner. Math. Soc. (MOS) 1970): primary 54 E 55; secondary 06 A 35, 06 A 23, 54 C 35.
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