Open cover of a metric space admits -partition of unity
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.
-embeddings, AR and ANR spaces.
-regular Cauchy completions.
-topological Cauchy completions.
Packing measures on ultrametric spaces
Pairwise closure-preserving collections and pairwise paracompactness
Pairwise monotonically normal spaces.
Pairwise monotonically normal spaces
We introduce and study the notion of pairwise monotonically normal space as a bitopological extension of the monotonically normal spaces of Heath, Lutzer and Zenor. In particular, we characterize those spaces by using a mixed condition of insertion and extension of real-valued functions. This result generalizes, at the same time improves, a well-known theorem of Heath, Lutzer and Zenor. We also obtain some solutions to the quasi-metrization problem in terms of the pairwise monotone normality.
Pairwise s-normal spaces
Pairwise weakly Hausdorff spaces
In this paper, we introduce and investigate the notion of weakly Hausdorffness in bitopological spaces by using the convergent of nets. Several characterizations of this notion are given. Some relationships between these spaces and other spaces satisfying some separation axioms are studied.
Pairwise weakly regular-Lindelöf spaces.
Paracompacité et espaces uniformes
Paracompactness in ordered spaces