The sizes of relatively compact -spaces
The relativization of Gryzlov’s theorem about the size of compact -spaces with countable pseudocharacter is false.
The space of rationals is not absolutely paracompact
The subspace of weak -points of
Let be the subspace of consisting of all weak -points. It is not hard to see that is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that is a -pseudocompact space for all .
The sup = max problem for the extent and the Lindelöf degree of generalized metric spaces, II
In [The sup = max problem for the extent of generalized metric spaces, Comment. Math. Univ. Carolin. The special issue devoted to Čech 54 (2013), no. 2, 245–257], the author and Yajima discussed the sup = max problem for the extent and the Lindelöf degree of generalized metric spaces: (strict) -spaces, (strong) -spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelöf degree of spaces having -diagonals and for the extent of spaces having point-countable bases...
The sup = max problem for the extent of generalized metric spaces
It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.
The union of two D-spaces need not be D
We construct from ⋄ a T₂ example of a hereditarily Lindelöf space X that is not a D-space but is the union of two subspaces both of which are D-spaces. This answers a question of Arhangel'skii.
The -property in
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
Three small results on normal first countable linearly H-closed spaces
We use topological consequences of PFA, MA(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.
Three technical tools in uniform spaces
Three Theorems on ...-m-Expandable Spaces.
Topological games and products I
Topological games and products, II
Topological games and products, III
Topological open problems in the geometry of Banach spaces.
Topological spaces compact with respect to a set of filters
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there...
Topologie fine et mesure de référence.
Topologie générale et espaces d'ultrafiltres
Total and absolute paracompactness
Transfinite cardinal dimension and separability
Two cardinal inequalities for functionally Hausdorff spaces
In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if is a functionally Hausdorff space, then .