The separation axioms
The sequentiality and the Fréchet-Urysohn property with respect to ultrafilters
The sequentiality is equivalent to the -Fréchet-Urysohn property
The shrinking property and the B-property in ordered spaces
The shrinking property of products of cardinals
The sizes of relatively compact -spaces
The relativization of Gryzlov’s theorem about the size of compact -spaces with countable pseudocharacter is false.
The smallest ideals in the two natural products on ßS.
The Smirnov compactification as a quotient space of the Stone-Čech compactification.
The Sorgenfrey line has no connected compactification
The space of complete subgraphs of a graph
The space of rationals is not absolutely paracompact
The star compactification.
The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ()
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 superextension of the closed unit interval is homeomorphic to the Hilbert cube
The Tensor Product of Continuous Lattices.
The Tychonoff product theorem for compact Hausdorff spaces does not imply the axiom of choice: A new Proof. equivalent propositions.
The undecidability of the existence of a non-separable normal Moore space satisfying the countable chain condition