Unit representation of semiorders II: The general case

Necessary and sufficient conditions under which semiorders on uncountable sets can be represented by a real-valued function constant threshold are known. We show that the proof strategy we used for constructing representations in case of denumerable adapted to case. use it give an alternative existence strict unit representations. In contrast countable case, admit representation do not necessarily nonstrict representation, conversely. By adapting representations, establish characterization representation. Conditions other special also obtained.