NOTES ON LEXIMORPHIC SPACES

摘要

A leximorphic space is a linearly ordered topological space (LOTS) with first and last points that is isomorphic to its Cartesian product given the lexicographic ordering. In this paper, examples of both countable and uncountable leximorphic spaces are detailed. Cardinality and consistency conditions characterizing leximorphic spaces are described. Finally, this paper settles an open question concerning the connectivity of leximorphic spaces.