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The product of two ordinals is hereditarily dually discrete

M.Á. Gaspar-Arreola, F. Hernández-Hernández (2012)

Commentationes Mathematicae Universitatis Carolinae

In Dually discrete spaces, Topology Appl. 155 (2008), 1420–1425, Alas et. al. proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In Products of certain dually discrete spaces, Topology Appl. 156 (2009), 2832–2837, Peng proved a number of partial results and left open the question of whether the product of two stationary subsets of ω 1 is dually discrete. We answer the first question affirmatively and as a consequence also give...

The sup = max problem for the extent and the Lindelöf degree of generalized metric spaces, II

Yasushi Hirata (2015)

Commentationes Mathematicae Universitatis Carolinae

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) p -spaces, (strong) Σ -spaces and semi-stratifiable spaces. In this paper, the sup = max problem for the Lindelöf degree of spaces having G δ -diagonals and for the extent of spaces having point-countable bases...

The sup = max problem for the extent of generalized metric spaces

Yasushi Hirata, Yukinobu Yajima (2013)

Commentationes Mathematicae Universitatis Carolinae

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.

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