@article{6fd2737c1ecf457e9fe3febecac2f5c0,
title = "Maximal elements of weakly continuous relations",
abstract = "A weaker than usual continuity property is defined for binary relations. Relations that have this property, along with certain transitivity properties, are shown to have maximal elements on compact sets. The results cover {"}interval orders,{"} the kind of relations that often characterize choice situations in which similar alternatives are indistinguishable.",
author = "Campbell, {Donald E.} and Mark Walker",
note = "Funding Information: * Campbell{\textquoteright}s research was financed by the Social Sciences and Humanities Council of Canada. We are grateful for discussions with Larry Epstein. {\textquoteright} Bergstrom [l] and Walker [S]. The theorem is elementary, as the proof in [S] demonstrates. If the relation{\textquoteright}s order properties are even weaker than acyclicity, but it is defined on a convex subset of a linear topological space and its upper-contour sets are convex. then several much deeper theorems are available to ensure the presence of maximal elements; see, for example, Sonnenschein [7]. Shafer and Sonnenschein 161. and Yannelis and Prabhakar 191.",
year = "1990",
month = apr,
doi = "10.1016/0022-0531(90)90013-A",
language = "English (US)",
volume = "50",
pages = "459--464",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "Academic Press Inc.",
number = "2",
}