A new characterization of Eberlein compacta
We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.
A new characterization of spaces with locally countable -networks
A new class of quasi-uniform spaces.
A new extension of countable compactness
A new form of fuzzy -compactness
A new form of -compactness is introduced in -topological spaces by -open -sets and their inequality where is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice . It can also be characterized by means of -closed -sets and their inequality. When is a completely distributive de Morgan algebra, its many characterizations are presented and the relations between it and the other types of compactness are discussed. Countable -compactness and the -Lindelöf property...
A new kind of compactness for topological spaces
A new Lindelöf space with points
We prove that implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality which has points . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.
A new ordered compactification.
A new semilattice of function algebras and its Boolean form on a lattice of groups.
A new way to find compact zero-dimensional first countable preimages of first countable compact spaces
A nice class extracted from -theory
We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, -stable and -monolithic. It is also established that any Sokolov compact space is Fréchet-Urysohn and the space is Lindelöf. We prove that any Sokolov space with a -diagonal has a countable network and obtain some cardinality restrictions on subsets...
A nice subclass of functionally countable spaces
A space is functionally countable if is countable for any continuous function . We will call a space exponentially separable if for any countable family of closed subsets of , there exists a countable set such that whenever and . Every exponentially separable space is functionally countable; we will show that for some nice classes of spaces exponential separability coincides with functional countability. We will also establish that the class of exponentially separable spaces has...
A non-Skorokhod topology on the Skorokhod space.
A non-Tychonoff relatively normal subspace
This paper presents a new consistent example of a relatively normal subspace which is not Tychonoff.
A normal space X for which X×I is not normal
A note on almost disjoint refinement
A note on Ascol's theorem for spaces of multifunctions.
A note on characterizations of compactness.
A note on collectionwise normality and product spaces
A note on compact metric spaces as remainders.