Ordered spaces with special bases

We study the roles played by four special types of bases (weakly uniform bases, omega-in-omega bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a G(delta)-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an omega-in-omega base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.