Open images of orderable spaces
Operation-separation axioms in bitopological spaces.
Order compatibility for Cauchy spaces and convergence spaces.
Ordered Cauchy spaces.
Ordered spaces with special bases
We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω 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 -diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered...
Ordinal products of topological spaces
The notion of the ordinal product of a transfinite sequence of topological spaces which is an extension of the finite product operation is introduced. The dimensions of finite and infinite ordinal products are estimated. In particular, the dimensions of ordinary products of Smirnov's [S] and Henderson's [He1] compacta are calculated.
Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency.